tag:blogger.com,1999:blog-279188842017-10-13T22:48:53.129-07:00GMAT MathsPrachi Pareekhhttps://plus.google.com/116441310095716126924noreply@blogger.comBlogger142125tag:blogger.com,1999:blog-27918884.post-52981887739655993072009-02-11T02:30:00.000-08:002009-02-11T03:54:32.643-08:00Data Sufficiency - 53Answer: 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 - sufficientPrachi Pareekhhttps://plus.google.com/116441310095716126924noreply@blogger.comtag:blogger.com,1999:blog-27918884.post-50406752098469394072009-02-11T02:18:00.000-08:002009-02-11T02:29:46.874-08:00Data Sufficiency - 52If 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 BPrachi Pareekhhttps://plus.google.com/116441310095716126924noreply@blogger.comtag:blogger.com,1999:blog-27918884.post-74556141141845577912009-01-12T01:03:00.000-08:002009-01-12T01:17:48.152-08:00Data Sufficiency - 51A 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 Prachi Pareekhhttps://plus.google.com/116441310095716126924noreply@blogger.comtag:blogger.com,1999:blog-27918884.post-37664536087958070692009-01-12T00:55:00.000-08:002009-01-12T01:02:21.301-08:00Problem Solving - 56A 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: Prachi Pareekhhttps://plus.google.com/116441310095716126924noreply@blogger.comtag:blogger.com,1999:blog-27918884.post-87736584248920369612008-11-18T23:39:00.000-08:002008-11-18T23:44:17.357-08:00Problem Solving - 55Which 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 ansPrachi Pareekhhttps://plus.google.com/116441310095716126924noreply@blogger.comtag:blogger.com,1999:blog-27918884.post-28275495445952425772008-11-18T23:33:00.000-08:002008-11-18T23:36:33.673-08:00Problem Solving - 54This 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 Prachi Pareekhhttps://plus.google.com/116441310095716126924noreply@blogger.comtag:blogger.com,1999:blog-27918884.post-4562846457782183692008-11-08T00:22:00.000-08:002008-11-08T00:34:00.234-08:00Problem Solving - 53A 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 Prachi Pareekhhttps://plus.google.com/116441310095716126924noreply@blogger.comtag:blogger.com,1999:blog-27918884.post-73634906113696416672008-11-07T23:47:00.000-08:002008-11-08T00:14:13.566-08:00Data Sufficiency - 50What 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 Prachi Pareekhhttps://plus.google.com/116441310095716126924noreply@blogger.comtag:blogger.com,1999:blog-27918884.post-89337683385635834192008-11-03T01:17:00.000-08:002008-11-03T01:28:51.288-08:00Problem Solving - 52A 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) Prachi Pareekhhttps://plus.google.com/116441310095716126924noreply@blogger.comtag:blogger.com,1999:blog-27918884.post-91433848650246735612008-11-03T01:08:00.000-08:002008-11-03T01:15:34.930-08:00Problem Solving - 51Each 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 Prachi Pareekhhttps://plus.google.com/116441310095716126924noreply@blogger.comtag:blogger.com,1999:blog-27918884.post-42473317794671836822008-10-16T02:48:00.000-07:002008-10-16T02:55:53.175-07:00Problem Solving - 50If 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 IIPrachi Pareekhhttps://plus.google.com/116441310095716126924noreply@blogger.comtag:blogger.com,1999:blog-27918884.post-30793499903384279742008-06-04T04:25:00.000-07:002008-10-15T00:37:10.688-07:00Data Sufficiency - 49Does 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 <=Prachi Pareekhhttps://plus.google.com/116441310095716126924noreply@blogger.comtag:blogger.com,1999:blog-27918884.post-80096296685754648042008-05-23T07:41:00.000-07:002008-05-23T08:36:48.775-07:00Problem Solving - 49Pumps 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)Prachi Pareekhhttps://plus.google.com/116441310095716126924noreply@blogger.comtag:blogger.com,1999:blog-27918884.post-51313245836205482852008-05-16T04:03:00.000-07:002008-05-16T04:46:57.553-07:00Set Theory - FormulasFormulas 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. NoPrachi Pareekhhttps://plus.google.com/116441310095716126924noreply@blogger.comtag:blogger.com,1999:blog-27918884.post-43496800164945278402008-05-06T09:41:00.000-07:002008-05-06T10:02:00.678-07:00Problem Solving - 48What 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.Prachi Pareekhhttps://plus.google.com/116441310095716126924noreply@blogger.comtag:blogger.com,1999:blog-27918884.post-78432596348175525792008-05-01T05:32:00.000-07:002008-10-15T00:38:34.415-07:00Data Sufficiency - 48In 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 Prachi Pareekhhttps://plus.google.com/116441310095716126924noreply@blogger.comtag:blogger.com,1999:blog-27918884.post-84953227294864786172008-04-27T06:19:00.000-07:002008-05-01T05:13:28.435-07:00Data Sufficiency - 47If 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 Prachi Pareekhhttps://plus.google.com/116441310095716126924noreply@blogger.comtag:blogger.com,1999:blog-27918884.post-25179561659880130142008-04-27T06:05:00.000-07:002008-04-27T06:18:11.516-07:00Data Sufficiency - 46What 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, Prachi Pareekhhttps://plus.google.com/116441310095716126924noreply@blogger.comtag:blogger.com,1999:blog-27918884.post-50853749316476960112008-04-20T21:35:00.000-07:002008-04-20T21:45:09.887-07:00Problem Solving - 47If 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 Prachi Pareekhhttps://plus.google.com/116441310095716126924noreply@blogger.comtag:blogger.com,1999:blog-27918884.post-59513034631588651552008-04-10T22:01:00.000-07:002008-04-20T21:34:58.162-07:00Problem Solving - 46A 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 Prachi Pareekhhttps://plus.google.com/116441310095716126924noreply@blogger.comtag:blogger.com,1999:blog-27918884.post-81613614301071643892008-03-19T05:18:00.000-07:002008-04-09T19:12:15.844-07:00Data Sufficiency - 45p^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 Prachi Pareekhhttps://plus.google.com/116441310095716126924noreply@blogger.comtag:blogger.com,1999:blog-27918884.post-66064270531433335732008-03-19T05:11:00.000-07:002008-04-27T19:32:21.758-07:00Problem Solving - 45If 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 = 5Prachi Pareekhhttps://plus.google.com/116441310095716126924noreply@blogger.comtag:blogger.com,1999:blog-27918884.post-5874100540632548932008-03-18T08:51:00.000-07:002008-03-18T08:59:28.760-07:00Problem Solving - 44Samar 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 Prachi Pareekhhttps://plus.google.com/116441310095716126924noreply@blogger.comtag:blogger.com,1999:blog-27918884.post-76539638557937714712008-02-05T00:41:00.000-08:002008-03-18T08:50:01.810-07:00Data Sufficiency - 44In 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 Prachi Pareekhhttps://plus.google.com/116441310095716126924noreply@blogger.comtag:blogger.com,1999:blog-27918884.post-32766510200237438862008-02-03T07:33:00.001-08:002008-02-05T00:39:34.693-08:00Data Sufficiency - 43In 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 segmentPrachi Pareekhhttps://plus.google.com/116441310095716126924noreply@blogger.com