GMAT Maths

Data Sufficiency - 53

2009-02-11T02:30:00.000-08:00

Answer: DFrom statement (1): Square root of a number less than 1 is also less than 1 - sufficientFrom statement (2): Reciprocal of any number less than 1 is greater than the number - sufficient

Data Sufficiency - 52

2009-02-11T02:18:00.000-08:00

If x is not equal to zero, is 1/x > 1 ?1) y/ x > y2) x^3 > x^2Answer: BFrom statement (1): y/x > y=> y > xy=> y(1-x) > 0y>0 when x is less than 1 or y<0 when x is greater than 1 ---- hence insufficientFrom statement (2): x^3 > x^2=> x^2(x-1) > 0=> x^2 >0 and x>1Since x>1, 1/x can not be greater than 1 ---- hence sufficientHence B

Data Sufficiency - 51

2009-01-12T01:03:00.000-08:00

A store purchases 20 coats that each cost an equal amount and then sold each of the 20 coats at an equal price, what was the store's gross profit on the 20 coats? 1). If the selling price per coat had been twice as much, the store's gross profit on the 20 coats would have been 2400 2). If the store selling price per coat had been $2 more, the store's gross profit on the 20 coats would have been

Problem Solving - 56

2009-01-12T00:55:00.000-08:00

A certain stock exchange designates each stock with a one- , two-,or three-letter code ,where each letter is selected from the 26 letters of the alphabet. If the letter may be repeated and if the same letters used in a different order constitute a different code, how many different stocks is it possible to uniquely designate with these codes? A) 2951 B) 8125 C) 15600 D) 15302 E) 18278 Answer:

Problem Solving - 55

2008-11-18T23:39:00.000-08:00

Which of the following fractions has a decimal equivalent that is a terminating decimal?A. 10/189 B. 15/196 C. 16/225 D. 25/144 E. 39/ 128Answer: ERULE: If denominator of a fraction has just the prime factors of 2 or 5 or both it is terminating otherwise not128 = 2*2*2*2*2*2*2 => has only factors of 2..hence the ans

Problem Solving - 54

2008-11-18T23:33:00.000-08:00

This year Henry will save a certain amount of his income, and he will spend the rest. Next year Henry will have no income, but for each dollar that he saves this year, he will have 1 + r dollars available to spend. In terms of r, what fraction of his income should Henry save this year so that next year the amount he was available to spend will be equal to half the amount that he spends this

Problem Solving - 53

2008-11-08T00:22:00.000-08:00

A student worked 20 days. For each of the amount shown (see attached table) in the first row of the table, second row gives the number of days the student earned that amount. Median amount of money earned per day for 20 days is? A) 96 B) 84 C) 80 D) 70 E) 48Answer: BMedian day = 20+1)/2 = 10.5 th -- money earned was 84= Average value of 10th and 11th day in the sequence = Median amount of

Data Sufficiency - 50

2008-11-07T23:47:00.000-08:00

What is the median number of employees assigned per project for the projects at Company Z? (1) 25 percent of the projects at Company Z have 4 or more employees assigned to each project. (2) 35 percent of the projects at Company Z have 2 or fewer employees assigned to each project.Answer: OA - CFrom Statement 1): It is given that 25 percent of the projects at Company Z have 4 or more employees

Problem Solving - 52

2008-11-03T01:17:00.000-08:00

A boat traveled up stream a distance of 90 miles at an average speed of (v-3) mph and then traveled the same distance downstream at an average speed of (v+3) mph. If the trip upstream took half an hour longer than the trip downstream, how many hours did it take the boat to travel downstream? (A) 2.5 (B) 2.4 (C) 2.3 (D) 2.2 (E) 2.1Answer: ATotal upstream time taken by boat to travel = 90/ (v-3)

Problem Solving - 51

2008-11-03T01:08:00.000-08:00

Each of the 10 machines works at the same constant rate of doing certain job. The amount of time needed by 10 machines, working together to complete the job is 16 hrs. How many hours are needed if only 8 machines working together were to complete the job? A. 18 B. 20 C. 22 D. 24 E. 26Answer: B10 machines, working at same constant rate, take time to complete a job = 16 hrsthus 1 machine takes

Problem Solving - 50

2008-10-16T02:48:00.000-07:00

If x = -|x|, then which one of the following statements could be true? I. x=0 II. x < 0III. x > 0A). none B). I only C). III only D). I and II E). II and IIIAnswer: DGiven x = - |x|We know that |x| >= 0=> -|x| = x <=0Thus inequalities represented by I and II

Data Sufficiency - 49

2008-06-04T04:25:00.000-07:00

Does the curve (x-a)^2 + (y-b)^2=16 intersect the y-axis ?(1) a^2+b^2>16 (2) a=|b|+5Answer: BThe given curve will intersect the y-axis when x=0Thus we get a^2 + (y-b)^2 = 16<=> a^2 + y^2 + b^2 - 2yb = 16<=> y^2 - 2yb + a^2 + b^2 -16 = 0In order to have real roots b^2 - 4ac >= 0=> 4b^2 - 4(1)(a^2 + b^2 -16) >=0=> a^2 <=16 From statement (1): Given that a^2 + b^2 > 16 No information about a^2 <=

Problem Solving - 49

2008-05-23T07:41:00.000-07:00

Pumps A, B, and C operate at their respective constant rates. Pumps A and B, operating simultaneously, can fill a certain tank in 6/5 hours, pumps A and C, operating simultaneously, can fill the tank in 3/2 hours; and pumps B and C, operating simultaneously, can fill the tank in 2 hours. How many hours does it take pumps A, B, and C, operating simultaneously, to fill the tank?A) 1/3B) 1/2C) 2/3D)

Set Theory - Formulas

2008-05-16T04:03:00.000-07:00

Formulas for three-component set problems:u = unionn = intersection1. For 3 sets A, B, and C: P(AuBuC) = P(A) + P(B) + P(C) – P(AnB) – P(AnC) – P(BnC) + P(AnBnC)2. No of persons in exactly one set: P(A) + P(B) + P(C) – 2P(AnB) – 2P(AnC) – 2P(BnC) + 3P(AnBnC)3. No of persons in exactly two of the sets: P(AnB) + P(AnC) + P(BnC) – 3P(AnBnC)4. No of persons in exactly three of the sets: P(AnBnC)5. No

Problem Solving - 48

2008-05-06T09:41:00.000-07:00

What is the angle formed by the diagonals of two adjacent surfaces of a cube? A) 45 B) 60 C) 90 D) 30 E) None of theseAnswer: BDraw from two adjacent surfaces of a cube the diagonals.Now see that it forms an equilateral triangle if we draw a third diagonal i.e diagonal in green color.Thus angles of the triangle will be 60 degrees; hence the answer.

Data Sufficiency - 48

2008-05-01T05:32:00.000-07:00

In the number line, are x and y on different sides of zero point?1). The distance from x to zero is equal to the distance from y to 1 2). The sum of the distance from x to zero and the distance from y to 1 is less than 1Answer: EFrom statement (1): |x-0|=|y-1| x = y-1 x = 1-y ....hence insufficientFrom statement (2): |x-0|+|y-1| less than 1= x+y-1 less than 1= x+1-y less than 1= -x+y-1 less

Data Sufficiency - 47

2008-04-27T06:19:00.000-07:00

If Line K in the XY-Plane has equation y=mx+b, where m and b are constants, what is the slope of K? 1. K is parallel to the line with equation y=(1-m)x+(b+1) 2. K intersects the line with equation y=2x+3 at the point (2,7)Answer: AFrom statement (1): y=(1-m)x+(b+1) has the same slope as y=mx+b. (Parallel lines have same slope) Thus 1-m = mimplies Slope of K=m=1/2 ---- Hence sufficientFrom

Data Sufficiency - 46

2008-04-27T06:05:00.000-07:00

What is the greatest common divisor of positive integers a and b?(1) a and b share exactly one common factor(2) a and b are both prime numbersAnswer: AFrom statement (1): we know that a and b have only one common factor, and we also know that all positive integers share the common factor 1 only, so we know it must be 1...hence sufficientFrom Statement (2): we know that a and b are both prime,

Problem Solving - 47

2008-04-20T21:35:00.000-07:00

If n is a positive integer and the product of all the integers from 1 to n, inclusive, is a multiple of 990, what is the least possible value of n? A) 10 B) 11 C) 12 D) 13 E) 14Answer: B990 is a multiple of n! implies it must contain all the prime factors of 990 Largest prime factor of 990 is 11 implies n! must have 11 as a factor Now since n! = 990x where x is integer it implies it can have

Problem Solving - 46

2008-04-10T22:01:00.000-07:00

A certain restaurant offers 6 kinds of cheese and 2 kinds of fruit for its dessert platter. If each dessert platter contains an equal number of kinds of cheese and kinds of fruit, how many different dessert platters could the restaurant offer? A) 8 B) 12 C) 15 D) 21 E) 27Answer: EKinds of platter: 1 cheese + 1 fruit Total = 6 * 2 = 12 types of platters 2 cheese + 2 fruitTotal = 6C2 * 2C2

Data Sufficiency - 45

2008-03-19T05:18:00.000-07:00

p^a * q^b * r^c * s^d = x, where x is a perfect square. If p, q, r, and s are prime integers, are they distinct? (1) 18 is a factor of ab and cd (2) 4 is not a factor of ab and cdAnswer: BOE: When a perfect square is broken down into its prime factors, those prime factors always come in "pairs." For example, the perfect square 225 (which is 15 squared) can be broken down into the prime factors

Problem Solving - 45

2008-03-19T05:11:00.000-07:00

If p is the smallest positive integer such that (p^3)/3920 is also an integer, what is the sum of the digits of p? (A) 5 (B) 7 (C) 9 (D) 11 (E) 13Answer: Am = p*p*p/ 3920m = p*p*p/ 2*2*2*2*5*7*7m = p*p*p/ [(4^2)*5*(7^2)]Hence p must be equal to 4*5*7 thus p = 140Hence sum of digits = 1+4+0 = 5

Problem Solving - 44

2008-03-18T08:51:00.000-07:00

Samar tried to type his new 7-digit phone number on a form, but what appeared on the form was 39269, since the '4' key on his computer no longer works. His secretary has decided to make a list of all of the numbers that could be Samar's new number. How many numbers will there be on the list?(A) 21 (B) 24 (C) 25 (D) 30 (E) 36Answer: AIt is clear from the question that

Data Sufficiency - 44

2008-02-05T00:41:00.000-08:00

In triangle ABC, AB has a length of 10 and D is the midpoint of AB. What is the length of line segment DC? (1) Angle C= 90(2) Angle B= 45Answer: AFrom statement (1): it is given that angle C = 90 degrees ...this implies that ABC is a right angle triangle with AB as the hypotenuse and DC as the median. We know that --- In all right triangles, the median on the hypotenuse is the half of the

Data Sufficiency - 43

2008-02-03T07:33:00.001-08:00

In the figure shown, what is the value of x? (1) The length of line segment of QR is equal to the length of line segment RS (2) The length of line segment of ST is equal to the length of line segment TUAnswer: C From statement (1): Length of line segment of QR is equal to the length of line segment RS ..this implies angle RQS = angle RSQ = p(say)From statement (2): Length of line segment

Data Sufficiency - 42

2008-01-31T23:18:00.000-08:00

Is a-3b an even number?1). b=3a+32). b-a is an odd numberAnswer: CFrom statement (1): Given that b=3a+3Thus a-3b=a-3(3a+3) = -8a-9 which may be even, odd, integer, non-integer, rational etc ... Hence insufficientFrom statement (2): Given that b-a is an odd number implies b is of the form b=(2k+1)+a where k is an integer Thus a-3b= a-3[(2k+1)+a] = -2a -6k-3 which may be even, odd, integer,

Problem Solving - 43

2008-01-30T18:25:00.000-08:00

If the sum of four consecutive positive integers a three digit multiple of 50, the mean of the these integers must be one of x possible values, where x= (A) 7 (B) 8 (C) 9 (D) 10 (E) more than 10Answer: CSuppose four integers are a, a+1, a+2 and a+3 Hence a + (a+1) + (a+2) + (a+3) = 4a+6Now 4a+6 will be a multiple of 50 i.e 4a+6=50m where m can take any

Data Sufficiency - 41

2008-01-30T18:07:00.000-08:00

Sania has a circular garden in her backyard. She puts poles A,B and C on the circumference of her garden. Then she ties ropes between these poles. Is length of one of the ropes is equal to the diameter of her garden? 1. Slope of line joining pole A and B is 3/4 and slope of line joining poles B and C is -4/3 2. Length of line joining pole A and B is 12 and length of line joining B and C is

Problem Solving - 42

2008-01-30T17:58:00.000-08:00

E is a collection of four odd integers and the greatest difference between any two integers in E is 4. The standard deviation of E must be one of how many numbers?(A) 3 (B) 4 (C) 5 (D) 6 (E) 7Answer: BSuppose the integers are 1, 3 and 5. Therefore the four integers can be:1, 5, 5, 51, 3, 5, 5 1, 3, 3, 51, 1, 5, 51, 1, 1, 51, 1, 3, 5Here two pairs have the same standard deviation. thus in all we

Data Sufficiency - 40

2008-01-23T00:12:00.000-08:00

In XY plane, does the line with equation y=3x+2 contain point (r,s)? 1) (3r + 2 - s)(4r + 9 - s) = 0 2) (4r - 6 - s)(3r + 2 - s) = 0Answer: CGiven that y = 3x+2 implies that does 3x+2-y = 0 contains the point (r,s) implies is (3r+2-s) = 0 ?From statement (1): (3r+2-s)(4r+9-s) = 0 implies either (3r+2-s) = 0 or (4r+9-s) = 0.Now when (3r+2-s)...the line passes through (r,s)When (4r+9-s) = 0 ...we

Problem Solving - 41

2008-01-20T07:57:00.000-08:00

If eleven consecutive integers are listed from least to greatest, what is the average (arithmetic mean) of the eleven integers? (1) The average of the first nine integers is 7. (2) The average of the last nine integers is 9.Answer: DLet the numbers be a, b, c, d, e, f, g, h , i, j, ki) For odd number of consecutive integers median = meanii)We also know that the median is the "middle" number in a

Data Sufficiency - 39

2008-01-20T07:44:00.000-08:00

If *triangle* denotes one of the four arithmetic operations addition, subtraction, multiplication and division, what is the value of 1 *triangle* 2 ? (1) n *triangle* 0 = n for all integers n. (2) n *triangle* n = 0 for all integers n.Answer: BFrom statement (1): *triangle* can be both positive or negative as n-0 = nn+0 = nHence insufficientFrom statement (2): *triangle* can only be negative in

Problem Solving - 40

2008-01-19T02:06:00.000-08:00

5 pieces of wood have an average (arithmetic mean) length of 124 centimeters and a median length of 140 centimeters. What is the maximum possible length in centimeters of the shortest piece of wood? A. 90 B. 100 C. 110 D. 130 E. 140Answer: B Shortest to Longest length ---- L1, L2, L3 = 140, L4, L5L1 + L2 + 140 + L4 + L5 = 5 * 124For L1 to be the maximum, L4 and L5 should be minimum L1=

Problem Solving - 39

2008-01-19T01:40:00.001-08:00

On a certain day, Tim invest $1,000 at 10 percent annual interest, compound annually, and Lana invested $ 2,000 at 5 percent annual interest, compound annually. The total amount of interest earned by Tim's investment in the first 2 years was how much greater than the total amount of interest earned by Lana's investment in the first 2 years? A. 5B. 15C. 50D. 100E. 105Answer: AAmount = P[1+(r/100)]

Problem Solving - 38

2008-01-19T01:40:00.000-08:00

6 machines, each working at the same constant rate, together can complete a certain job in 12 days, How many additional machines, each working at the same constant rate, will be needed to complete the job in 8 days? A. 2 B. 3 C. 4 D. 6 E. 8Answer: B6 machines take = 12 days. Therefore 1 machine = 12*6 days. 8 days will take = (12*6)/8 = 9 machines. No of additional machines required = 9-6

Problem Solving - 37

2008-01-15T22:29:00.000-08:00

Of the 800 companies in Company X, 70% have been with the company for at least 10 years. If y of these "long-term" members were to retire, and no other employee changes were to occur, what value of y would reduce the percent of "long-term" employees in the company to 60%. A) 200 B) 160 C) 112 D) 80 E) 56Answer: AAssume y=xThe number of people working more than 10 years = 70% of 800 = 560Hence (

Problem Solving - 36

2008-01-15T11:16:00.000-08:00

Equal amounts of water were poured into two empty jars of different capacities, which made one jar 1/4 full and the other jar 1/3 full. If the water in the jar with lesser capacity is then poured into the jar with the greater capacity, what fraction of the larger jar will be filled with water? A. 1/7 B. 2/7 C. 1/2 D. 7/12 E. 2/3Answer: CThe jar that is 1/3 full is smallerwater in jar 1 = water

Problem Solving - 35

2008-01-14T05:42:00.000-08:00

The rate of a certain chemical reaction is directly proportional to the square of the concentration of chemical A present and inversely proportional to the concentration of chemical B present. If the concentration of chemical B is increased by 100 percent, which of the following is closest to the percent change in the concentration of chemical A required to keep the reaction rate unchanged?A.

Problem Solving - 34

2008-01-14T05:31:00.000-08:00

A certain library assesses fines for overdue books as follows. On the first day that a book is overdue, the total fine is $0.10. For each additional day that the book is overdue the total fine is either increased by $0.30 or double, whichever results in the lesser amount. What is the total fine for a book on the fourth day it is overdue? A. $0.60B. $0.70C. $0.80D. $0.90E. $1.00Answer: BDay 1 =

Data Sufficiency - 38

2008-01-11T21:55:00.001-08:00

If q is a integer, is q^4 a multiple of 64? (1) q^4 is not a multiple of 128. (2) q^2 has 27 factors, 7 of which are less than or equal to 10Answer: AOE:From statement (1): Given q is an integer, thus q can be written as product of distinct prime factors, where the power of 2 must be a whole number(a non-negative integer). This implies that the power of 2 in the prime factorization of q^4 must

Problem Solving - 33

2008-01-11T10:37:00.000-08:00

A hiker walking at a constant rate of 4 miles per hour is passed by a cyclist traveling in the same direction along the same path at a constant rate of 20 miles per hour. The cyclist stops to wait for the hiker 5 minutes after passing her, while the hiker continue to walk at her constant rate. How many minutes must the cyclist wait until the hiker catches up?A. 20/3 B. 15 C. 20 D. 25 E. 80/

Data Sufficiency - 37

2008-01-11T10:23:00.000-08:00

At least 100 students at a certain high school study Japanese. If 4 percent of the students who study French also study Japanese, do more students at the school study French than Japanese? 1). 16 students at the school study both French and Japanese.2). 10 percent of the students at the school who study Japanese also study French.Answer: BFrom statement (1):16 students study both French and

Problem Solving - 32

2008-01-11T10:11:00.000-08:00

List K consists of 12 consecutive integers, if -4 is the least integer in list K, what is the range of the positive integers in the list K?A. 5 B. 6 C. 7 D. 11 E. 12Answer: BThe least number in the list is -4, thus the list is: -4,-3,-2,-1, 0, 1, 2, 3, 4, 5, 6, 7Positive integers in the above list: 1, 2, 3, 4, 5, 6, 7Therefore the range of the positive integers is 7-1 = 6

Data Sufficiency - 36

2008-01-11T09:50:00.000-08:00

If set S consist of the numbers 1, 5, -2, 8, and n, is 0 less than n less than 7 ? 1). the median of the numbers in S is less than 5.2). the median of the numbers in S is greater than 1Answer: CFrom statement (1): Median will be less than 5 only if n is located below 5 Thus the median will either be 1 if n less than 1 or n if 1 less than n less than 5 Hence in both cases n is less than 5 but it

Data Sufficiency - 35

2008-01-08T18:12:00.000-08:00

Data Sufficiency - 34

2008-01-08T17:55:00.000-08:00

In the xy-plane, at what two points does the graph of y=(x+a)(x+b) intersect the x-axis? 1). a+b= -12). The graph intersects the y-axis at (0,-6)Answer: CFrom Statement (1) -- a+b = -1...no information about a and b ...hence insufficient From Statement (2) -- If x = 0 the y = -6 thus ab = 6....insufficient Taking statements (1) and (2) together: (x+a)*(x+b)=0x^2+(a+b)x+ab=0 Hence x=-3, x=

Problem Solving - 31

2007-12-18T17:17:00.000-08:00

A certain characteristic in a large population has a distribution that is symmetric about the mean m.If 68 percent of the distribution lies within one Standard Deviation d of the mean, what percent of the distribution is less than m+d?A. 16%B. 32%C. 48%D. 84%E. 92%Answer: D In a normal bell curved distribution, 50% are below the mean and 50% are over itIf 68% are distributed within 1 S.D of the

Data Sufficiency - 33

2007-11-27T05:34:00.001-08:00

Is |x - 1| less than 1 ?1). (x - 1)^2 less than and equal to 12). x^2 - 1 greater than 0Answer: E |x-1| less than 1 is only true when 0 less than x less than 1From statement (1): (x-1)^2<=1 True when 0<=x<=2 If x=0.5, then |x-1| less than 1 is true If x=2, then |x-1| less than 1 is not trueHence insufficientFrom statement (2): x^2>1 means x>1 and x<-1 True when x=1.5, but not when x=3Hence

Problem Solving - 30

2007-11-27T05:26:00.000-08:00

Which of the following is always equal to sqrt (9 + x^2 - 6x)? a) x - 3 b) 3 + x c)|3 - x| d)|3 + x| e) 3 - xAnswer: C sqrt (9+x^2-6x)= sqrt( (3-x)^2 )= |3-x|

Data Sufficiency - 32

2007-11-27T05:15:00.000-08:00

What is the value of x?1) (-x)^3 = -x^32) (-x)^2 = -x^2Answer: BFrom statement (1):if x = 0 both sides are equalif x = 1 both sides are again equal {(-1)^3 = -1 & -1^3 = 1}=> x = 0 or x = 1Hence insufficientFrom statement (2): x can only be zero because the square of a number other than zero cannot be negative{(-1)^2 = 1 which is not equal to -(1)^2)} => from above it is sufficient to say that x

Data Sufficiency - 31

2007-11-05T08:46:00.000-08:00

Is |x - 1| less than 1 ?(1). (x - 1) ^2 less than and equal to 1(2). (x^2) - 1 greater than 0Answer: EFrom statement (1): (x - 1) ^2 less than and equal to 1 Now this is true only if 0 is less than and equal to x and x is less than and equal to 2. (We know that (x - 1) ^2 less than 1 is only true when 0 is less than x and x is less than 2)When we take x = 0.5, then |x-1| less than 1 is

Statistics - Rules and Tips!

2007-10-23T19:45:00.000-07:00

1. Mean Average = total of quantities / number of quantities2. The median is the "middle" number in a group (when arranged in ascending or descending order) consisting of an odd number of numbers, and the average of the two middle numbers if there are an even number of numbers3. For a set of consecutive integers, the median is the the average of the first and the last integer4. Mode is the

Problem Solving - 29

2007-10-03T04:20:00.000-07:00

IF s is the product of integers from 100 to 200, inclusive, and t is the product of integers from 100 to 201, inclusive, what is 1/s + 1/t in terms of t?A. (201) ^2 / tB. [(202) (201)]/tC. 201/tD. 202/tE. [(202) (201)]/(t^2)Answer: DGiven s = 100 * ... * 200Given t = 100 * ... * 200 * 201=> s = t/201Hence 1/s + 1/t = 201/t + 1/t = 202/t

Problem Solving - 28

2007-10-03T04:07:00.000-07:00

According to the directions on a can of frozen orange juice concentrate, 1 can of concentrate is to be mixed with 3 cans of water to make orange juice. How many 12-ounce cans of the concentrate are required to prepare 200 6-ounce servings of orange juice? A. 25 B. 34 C. 60 D. 67 E. 100Answer: A4 cans of orange juice need 1 can of concentrate. 200 cans 6-ounce of orange juice need 50 cans 6-ounce

Problem Solving - 27

2007-10-03T04:02:00.000-07:00

In the addition table above, what is the value of m+n? (A) -19 (B) 4 (C) 5 (D) 6 (E) 22Answer: Cm = z + 4 n = y + e m + n = z + 4 + y + e = (z+e) + (4+y) = 10 + (-5) = 5

Problem Solving - 26

2007-10-03T03:54:00.000-07:00

n = 2*3*5*7*11*13/77k ...... If n is an integer and then which of the following could be the value of k? (A) 22 (B) 26 (C) 35 (D) 54 (E) 60 Answer: Bn = 2*3*5*7*11*13/77k = 2*3*5*7*11*13/7*11*k = 2*3*5*13/k => k must be the product of any combination of product of these numbers. From the given choices only 26 ------ (2*13) fits.

Problem Solving - 25

2007-10-03T03:44:00.000-07:00

Two canoe riders must be selected from each of two groups of campers. One group consists of three men and one woman, and the other group consists of two women and one man. What is the probability that two men and two women will be selected?(A) 1/6(B) 1/4(C) 2/7(D) 1/3(E) 1/2 Answer: E1st Group: 3 Men, 1 Woman 2nd Group: 1 Man, 2 Women Total number of ways of selection: 4C2 * 3C2 = 18 No of ways

DS Question - 30

2007-06-30T12:12:00.000-07:00

If q is a multiple of prime numbers, is q a multiple of r? 1) r is less than 42) q = 18Answer: EFrom Statement (1) -- q can be positive and r can be negative. r can also be a real number but not necessarily an integer.Hence insufficient. From Statement (2) -- q = 18.But r can be negative or can be positive.r can also be a real number not an integerHence insufficientTaking both statements (1) and

DS Question - 29

2007-06-26T19:30:00.000-07:00

If x and y are integers, does IxI = y ? (1) (y^2 - x^2) = 0 (2) xy/(x+y) = 0Answer: BStatement (1) insufficient -- y can take any value i.e can be +ve or -ve. We cannot assume y to be +ve. Therefore y may or may not be equal to x Statement (2) sufficient -- xy/(x+y) = 0 => xy = 0 => x = 0 or y = 0 In case x = 0, then y cannot be equal to 0. Hence y cannot be equal to x. In case y = 0, then x

DS Question - 28

2007-06-26T19:05:00.000-07:00

Is the three-digit number n less than 550? 1) The product of the digits in n is 30 2) The sum of the digits in n is 10Answer: CFrom statement (1) : the factors of 30 are 1,2,3,5,6,10,15,30 Now because the number must be digits (single number) we do not need to consider 10,15 and 50 Now if the hundreds digit of the 3-digit number = any digit among the 1,2,3 digits ---> answer to the question is

Problem Solving - 24

2007-06-26T18:57:00.000-07:00

On his drive to work, Bob listens to one of three radio stations, A,B, or C. He first turns to A. If A is playing a song he likes, he listens to it; if not, he turns to B. If B is playing a song he likes, he listens to it; if not, he turns to C. If C is playing a song he likes, he listens to it; if not, he turns off the radio. For each station , the probability is 0.30 that any given moment the

Problem Solving - 23

2007-06-26T18:41:00.000-07:00

If x is an integer divisible by 15 but not divisible by 20, then x CANNOT be divisible by which of the following? (A) 6 (B) 10 (C) 12 (D) 30 (E) 150Answer: Cx is divisible by 15 -> x is divisible by 3 and 5 x is not divisible by 20 -> x is not divisible by 4Now because x is divisible by 15, it has 3 and 5 as factors and because x is not divisible by 20, it definitely does not have 4 as a factor .

Problem Solving - 22

2007-06-26T11:43:00.001-07:00

A certain restaurant offers 6 kinds of cheese and 2 kinds of fruit for it dessert platter. If each dessert platter contains an equal number of kinds of cheese and kinds of fruit, how many different dessert platters could the restaurant offer? (A) 8 (B) 12 (C) 15 (D) 21 (E) 27Answer: EThere are two kinds of platter ---- 1 cheese + 1 fruit Total types of platter -- 6 * 2= 12 ---(1)For 2 cheese + 2

DS Question - 27

2007-06-01T05:12:00.000-07:00

The area of a parallelogram is 100. What is the perimeter of the parallelogram ? 1) the base of the parallelogram is 10 2) one of the angles of the parallelogram is 45 degreeAnswer: C From (1) - For a parallelogram, Area = Base*Height => Height = 10 - There are infinite ways to draw a parallelogram with 100 as area, as long as the height is 10 units.( parallelograms with varying slants from 1 to

Manhattan Challenge Problem of the week! - 05/28/07

2007-06-01T05:05:00.000-07:00

Baseball's World Series matches 2 teams against each other in a best-of-seven series. The first team to win four games wins the series and no subsequent games are played. If you have no special information about either of the teams, what is the probability that the World Series will consist of fewer than 7 games?(A) 12.5%(B) 25%(C) 31.25%(D) 68.75%(E) 75%Answer: DOE - In order to determine the

Manhattan Challenge Problem of the week! - 05/21/07

2007-06-01T04:48:00.000-07:00

Edwin is planning to drive from Boston to New Orleans. By what percent would his travel time be reduced if Edwin decides to split the driving time equally with his friend George, instead of making the trip alone?(1) The driving distance from Boston to New Orleans is 1500 miles.(2) George’s driving speed is 1.5 times Edwin’s driving speed.Answer: BOE - The question asks for the percent decrease in

Manhattan Challenge Problem of the week! - 04/30/07

2007-06-01T04:37:00.000-07:00

How many terminating zeroes does 200! have?(A) 40(B) 48(C) 49(D) 55(E) 64Answer : C OE - To determine how many terminating zeroes a number has, we need to determine how many times the number can be divided evenly by 10. (For example, the number 404000 can be divided evenly by 10 three times, as follows: 404000/10 = 4040040400/10 = 40404040/10 = 404We can see that the number has three terminating

Manhattan Challenge Problem of the week! - 04/23/07

2007-05-31T23:56:00.000-07:00

Which of the following sets includes ALL of the solutions of x that will satisfy the equation: Answer: OA - C OE - One way to solve equations with absolute values is to solve for x over a series of intervals. In each interval of x, the sign of the expressions within each pair of absolute value indicators does not change. In the equation Ix-2I - Ix-3I = Ix-5I , there are 4 intervals of interest:

Manhattan Challenge Problem of the week! - 16/04/07

2007-05-31T23:26:00.000-07:00

x and y are positive integers. , what is the value of xy? (A) 48(B) 36(C) 24(D) 18(E) 12Answer: OA - E5^x - 5^y = 2^(y-1) * 5^(x-1)Divide both sides by 5^(x-1)....we get[5^x/ 5^(x-1)] - [5^y/ 5^(x-1)] = 2^(y-1)Simplifying the first tem we get5 - [5^x/ 5^(x-1)] = 2^(y-1)Add [5^y/ 5^(x-1)] to both sides...we get5 = 2^(y-1) + [5^y/ 5^(x-1)] We know that 2^(y-1) and [5^y/ 5^(x-1)] are positive and

Problem Solving - 21

2007-05-03T11:37:00.000-07:00

Mrs. Napueta has been given film vouchers. Each voucher allows the holder to see a film without charge. She decides to distribute them among her four nephews so that each nephew gets at least two vouchers. How many vouchers has Mrs. Napueta been given if there are 120 ways that she could distribute the vouchers?(A) 13(B) 14(C) 15(D) 16(E) more than 16Answer: CFormula - Number of ways of

DS Question - 26

2007-05-01T10:18:00.000-07:00

Is 5^k less than 1,000?(1) 5^(k-1) greater than 3,000(2) 5^(k-1) = 5^k - 500 Answer: DFrom statement (1) - 5^(k-1) is greater than 3000 => 5^k/5 is greater than 3000=> 5^k is greater than 15000Hence sufficientFrom statement (2) - 5^(k-1) = 5^k - 500=> 5^(k-1) = 5^k - 500 => 5^k - 5^(k-1) = 500 => 5^k(1- 5^-1) = 500 => 5^k(4/5) = 500 => 5^k = 2500/4 = 625 Therefore 5^k is less than 1000Hence

DS Question - 25

2007-04-28T09:40:00.000-07:00

Is 5^k less than 1,000? (1) 5^(k-1) is less than 3000(2) 5^(k-1) = 5^k - 500Answer: BFrom statement (1) - It is given that 5^(k-1) less than 3000=> 5^k/5 less than 3000=> 5^k less than 15000=> 5^k could be either more than 1,000 or less than 1,000. Hence insufficient From statement (2) - It is given that 5^(k-1) = 5^k - 500=> 5^k/5 = (5^k) - 500 => 5^k = 5*(5^k) - 2500 => (5-1)*5^k = 2500 => 4*5^

DS Question - 24

2007-04-28T09:24:00.000-07:00

What is the 999th term of the series S ?(1) The first 4 four terms of S are (1 + 1)² , (2 + 1)² , (3 + 1)² , and (4 + 1)².(2) For every x, the xth term of S is (x + 1)².Answer: BFrom statement (1) - It is given that the 1st 4 four terms of S are (1 + 1)² , (2 + 1)² , (3 + 1)² , and (4 + 1)². We only know the first four terms. We cannot assume that terms following the first 4 terms will be like --

Problem Solving - 20

2007-04-20T22:27:00.000-07:00

What is the area of the trapezoid pictured to the right? (A) 22.5 (B) 24 (C) 27 (D) 45 (E) 54Answer: ASince the triangle is a right isosceles triangle, the other side of the triangle (the height of the trapezoid) must also be 3. The top base if the trapezoid must be 6 since it is the opposite side of a rectangle.The area of a trapezoid = 1/2 (sum of parallel sides) × (distance between the

Problem Solving - 19

2007-04-11T04:17:00.001-07:00

How many 5 digit numbers can be created if the following terms apply: the leftmost digit is even, the second is odd, the third is a non even prime and the fourth and fifth are two random digits not used before in the number?a) 2520b) 3150c) 3360d) 6000e) 7500Answer: Given OA - A is incorrect ... ans is 2688 which is not an option in the choices...When 2nd and 3rd digit gets repeated:The first

DS Question - 23

2007-04-11T03:48:00.000-07:00

If x is a positive integer, then how many factors does x have ?(1) x is divisible by one more positive integer than 3^4 is.(2) x is the product of three different prime numbersAnswer: DFrom statement (1) - x has 5 factors 1, 3, 9, 27, 81. Adding one more factor from statement (1) makes total number of factors to be six.Thus x has 6 factors.Hence sufficientFrom statement (2) - x = abc where a, b,

Manhattan Challenge Problem of the week! - 09/04/07

2007-04-10T10:55:00.000-07:00

Stephanie, Regine, and Brian ran a 20 mile race. Stephanie and Regine's combined times exceeded Brian's time by exactly 2 hours. If nobody ran faster than 8 miles per hour, who could have won the race? I. Stephanie II. Regine III. Brian (A) I only(B) II only(C) III only(D) I or II only(E) I, II, or IIIAnswer: DLet the race time of Stephanie = SLet the race time of Regine = R Let the race time of

Manhattan Challenge Problem of the week! - 02/04/07

2007-04-10T10:48:00.000-07:00

Triangle A has one side of length x. If (x^8) ^ 1/2 = 81 , what is the perimeter of Triangle A?1) Triangle A has sides whose lengths are consecutive integers2) Triangle A is NOT a right triangle(A) Statement (1) alone is sufficient, but statement (2) alone is not sufficient.(B) Statement (2) alone is sufficient, but statement (1) alone is not sufficient. (C) BOTH statements TOGETHER are

DS Question - 22

2007-03-29T12:46:00.000-07:00

n is a positive integer. What is the remainder when n is divided by 6? (1) n is a multiple of 3. (2) When n is divided by 2, the remainder is 1.Answer: CFrom statement (1) - n can be 3, 6, 9, 12... Therefore: (i) If n is odd, the reminder is 3 on dividing by 6. (ii) If n is even, the reminder is 0 on dividing by 6. Hence Insufficient. From statement (2) - When n is divided by 2, the remainer is

DS Question - 21

2007-03-28T10:21:00.000-07:00

If 20 Swiss Francs is enough to buy 9 notebooks and 3 pencils, is 40 Swiss Francs enough to buy 12 notebooks and 12 pencils? (1) 20 Swiss Francs is enough to buy 7 notebooks and 5 pencils. (2) 20 Swiss Francs is enough to buy 4 notebooks and 8 pencils.Answer : B It is given that 9x + 3y <= 20It is required to prove that 12x + 12y <= 40 or 6x + 6y <= 20Hence basically the question asks that

Problem Solving - 18

2007-03-28T10:02:00.000-07:00

If n is a positive integer and n^2 is divisible by 72, then the largest possible positive integer that must divide n isA) 6 B) 12 C) 24 D) 36 E) 48Answer : BFocus primarily on the word "must" and after that shift your focus to the word "largest"n^2 = 72q = 36*2q = 6^2*2q , where 2q must be the square of a number q = 2p^2 , where p is a +ve integer Hence n = 12p As such 12 is the largest possible

Manhattan Challenge Problem of the week! - 26/03/07

2007-03-28T09:37:00.000-07:00

If 3x - 2y - z = 32 + z and (3x) ^ 1/2 - (2y + 2z) ^ 1/2 = 4 , what is the value of x + y + z ?(A) 3(B) 9(C) 10(D) 12(E) 14Answer: EEach equation represents one of the elements in the common quadratic form:Rewrite the given equation as follows: 3x - 2y - z = 32 + z3x - (2y + 2z) = 32Then, notice its relationship to the second given equation: (3x) ^ 1/2 - (2y + 2z) ^ 1/2 = 4 The second equation is

Probelm Solving - 17

2007-03-23T10:34:00.000-07:00

On the coordinate plane (6, 2) and (0, 6) are the endpoints of the diagonal of a square. What is the distance between point (0, 0) and the closest vertex of the square?(A) 1/sqrt (2)(B) 1(C) sqrt (2)(D) sqrt (3)(E) 2*sqrt (3)Answer : CMidpoint of the diagonal = (3,4)Slope of the diagonal = -2/3Slope of the other diagonal is the negative reciprocal of the first diagonal = 3/2 Let one of the

DS Question - 20

2007-03-23T07:20:00.000-07:00

Series of A(n) is such that A(n) = A(n-1) / n. How many elements of the series are bigger than 1/2 ? (1) A(2) = 5 (2) A(1) - A(2) = 5Answer : DFrom statement (1) --- A(2) = 5 . It is given that A(n) = A(n-1) / n.Hence A(2) = A(1) / 2 => A(1) = 10 A(2) = 5 =A(3) = A(2) / 3 = 5 /3 A(4) = A(3) / 4 = 5 /( 3 * 4) = 5 /12Hence statement (1) alone is sufficient to aswer the question. From statement

Problem Solving - 16

2007-03-22T05:26:00.001-07:00

Six mobsters have arrived at the theater for the premiere of the film “Goodbuddies.” One of the mobsters, Frankie, is an informer, and he's afraid that another member of his crew, Joey, is on to him. Frankie, wanting to keep Joey in his sights, insists upon standing behind Joey in line at the concession stand. How many ways can the six arrange themselves in line such that Frankie’s requirement is

Mnahattan Challenge Problem of the week! - 21/03/07

2007-03-22T05:03:00.000-07:00

For a three-digit number xyz, where x, y, and z are the digits of the number, the function f(xyz) = 5x2y3z. If f(abc) = 3 * f(def), what is the value of abc - def? (A) 1(B) 2(C) 3(D) 9(E) 27Answer : AIt is given in the question that .It is obvious that the digits b, c, e, f are integers from 0 to 9 whereas that the digits a and d are integers from 1 to 9 (can't be equal to 0 because they are in

DS Question - 19

2007-03-21T07:56:00.000-07:00

Is x = square root (x^2) if(1) x = even(2) 13 is less than x is less than 17Answer: BFrom Statement (1) -- x = even . Always remember square root (x^2) = mod x.E.g - squareroot (-4 ^ 2) = 4 ; suareroot (4^ 2) = 4. Hence 1 is insufficient.From Statement (2) --13 is less than x is less than 17 implies that x can be 14, 15 or 16 ..hence X IS POSITIVE...Hence sufficient.Note : Is x = square root (x^

Manhattan Challenge Problem of the week ! - 13/26/07

2007-03-14T21:30:00.000-07:00

x years ago, Cory was one fifth as old as Tania. In x years, Tania will be twice as old as Cory. What is the ratio of Cory's current age to Tania's current age?(A) 7:23(B) 9:17(C) 5:13(D) 3:7(E) 11:15Answer : C Use a chart to keep track of the ages in this problem: x years ago NOW in x years Corey C - x C C + x

DS Question - 18

2007-03-11T09:58:00.000-07:00

Each of the 25 balls in a certain box is either red, blue or white and has a number from 1 to 10 painted on it. If one ball is to be selected at random from the box, what is the probability that the ball selected will either be white or have an even number painted on it?1) The probability that the ball will both be white and have an even number painted on it is 0.2) The probability that the ball

DS Question - 17

2007-03-06T23:50:00.000-08:00

In the xy-plane, the line k passes through the origin and through the point (a, b), where ab is not equal to 0. Is b positive ?1). The slope of line k is negative.2). a is less than bAnswer : CIt is given that the line passes through (0,0) and (a,b)So it's slope = (b-0)/(a-0) = b/aStatement (1) ---- Slope of line k is (-ve).=> (b/a) less than 0 implies a and b are of opposite signs.From the

DS Question - 16

2007-03-06T22:42:00.000-08:00

IS x^4 + y^4 > z^4 ? a) x^2 + y^2 > z^2 b) x + y > zAnswer - E(1) x^2 + y^2 > z^2, when squared, gives the stated equation.From this we cannot conclude definitively whether x^4 + y^4 > z^4 because the equation contains (2x^2 * y^2). If this is removed, then x^4 + y^4 may or may not be > z^4.Thus insufficient..e.g - 2+3+4 > 5 --- if we remove 1 number from the left hand side of the

Manhattan Challenge Problem of the week! - 7 march 07

2007-03-06T21:03:00.000-08:00

The function f(n) = the number of factors of n. If p and q are positive integers and f(pq) = 4, what is the value of p?(1) p + q is an odd integer(2) q is less than p(A) Statement (1) alone is sufficient, but statement (2) alone is not sufficient.(B) Statement (2) alone is sufficient, but statement (1) alone is not sufficient. (C) BOTH statements TOGETHER are sufficient, but NEITHER statement

DS Question - 15

2007-03-02T00:31:00.000-08:00

A certain clothing manufacturer makes only two types of men's blazer: cashmere and mohair. Each cashmere blazer requires 4 hours of cutting and 6 hours of sewing. Each mohair blazer requires 4 hours of cutting and 2 hours of sewing. The profit on each cashmere blazer is $40 and the profit on each mohair blazer is $35. How many of each type of blazer should the manufacturer produce each week in

Problem Solving - 15

2007-03-02T00:28:00.000-08:00

During a behavioral experiment in a psychology class, each student is asked to compute his or her lucky number by raising 7 to the power of the student's favorite day of the week (numbered 1 through 7 for Monday through Sunday respectively), multiplying the result by 3, and adding this to the doubled age of the student in years, rounded to the nearest year. If a class consists of 28 students,

Manhattan Challenge Problem of the week ! - 02/26/07

2007-03-02T00:21:00.000-08:00

What is xy? (1) (2) (A) Statement (1) alone is sufficient, but statement (2) alone is not sufficient.(B) Statement (2) alone is sufficient, but statement (1) alone is not sufficient. (C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.(D) Each statement ALONE is sufficient.(E) Statements (1) and (2) TOGETHER are NOT sufficient. Answer : A

DS Question - 14

2007-02-26T09:48:00.000-08:00

How many odd integers are greater than integer X and less than the integer Y? 1). there are 12 even integers greater than X and less than Y 2). there are 24 integers greater than X and less than Y Answer -- BFrom statement 1) -- We cannot determine about both X, Y being even or odd. ... hence insufficient From statement 2) -- There are 24 integers between X and YLet it start with an even

Problem solving - 14

2007-02-26T08:55:00.000-08:00

Larry, Michael, and Doug have five donuts to share. If any one of the men can be given any whole number of donuts from 0 to 5, in how many different ways can the donuts be distributed?(A) 21(B) 42(C) 120(D) 504(E) 5040Answer - A -- generally answer for such questions is the sum of the series of integers from 1 to n+1 where n = number of items to be distributed. In this ques n = 5, thus the answer

Problem solving - 13

2007-02-22T09:26:00.000-08:00

If n is an integer from 1 to 96, what is the probability for n*(n+1)*(n+2) being divisible by 8? A) 25% B) 50% C) 62.5% D) 72.5% E) 75%Answer - Cn is even - anytime n is even, it is divisible by 8 total nos using sequence theorm 96 = 2 + (#-1) 2, hence # = 48 n is odd - again 48 no but in 1-8, only one combination is divisible by 8, when n is 7,15, 22... hence 12 cases probalility = possible

Problem solving - 12

2007-02-22T09:17:00.000-08:00

If p is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of p? A. 10B. 12 C. 14D. 16E. 18Answer -- CP = 1*2*3*.....*30if u factorize P, what is the power of 3 ?So we have to find out how many 3's are there in he product.As is known 3,6,9,12,15,18,21,24,27,30 is total count of 10 numbersbut 9 = 3*3 thus 1 extra 318 = 3*3*2 thus 1 extra

Problem solving - 11

2007-02-22T09:08:00.001-08:00

A number is selected at random from first 30 natural numbers. What is the probability that the number is a multiple of either 3 or 13?(A) 17/30(B) 2/5(C) 7/15(D) 4/15(E) 11/30Answer -- BThe first 30 natural nos are 1,2,3.....28,29,30.There are 10 multiples of 3 in the above range and there are 2 multiples of 13 in the same range.Hence there are total 12 i.e (10+2) nos which can be either a