Answer: D
From statement (1): Square root of a number less than 1 is also less than 1 - sufficient
From statement (2): Reciprocal of any number less than 1 is greater than the number - sufficient
Showing posts with label Data Sufficiency. Show all posts
Showing posts with label Data Sufficiency. Show all posts
Wednesday, February 11, 2009
Data Sufficiency - 53
Answer: D
From statement (1): Square root of a number less than 1 is also less than 1 - sufficient
From statement (2): Reciprocal of any number less than 1 is greater than the number - sufficient
Data Sufficiency - 52
If x is not equal to zero, is 1/x > 1 ?
1) y/ x > y
2) x^3 > x^2
Answer: B
From statement (1): y/x > y
=> y > xy
=> y(1-x) > 0
y>0 when x is less than 1 or y<0 when x is greater than 1 ---- hence insufficient
From statement (2): x^3 > x^2
=> x^2(x-1) > 0
=> x^2 >0 and x>1
Since x>1, 1/x can not be greater than 1 ---- hence sufficient
Hence B
1) y/ x > y
2) x^3 > x^2
Answer: B
From statement (1): y/x > y
=> y > xy
=> y(1-x) > 0
y>0 when x is less than 1 or y<0 when x is greater than 1 ---- hence insufficient
From statement (2): x^3 > x^2
=> x^2(x-1) > 0
=> x^2 >0 and x>1
Since x>1, 1/x can not be greater than 1 ---- hence sufficient
Hence B
Monday, January 12, 2009
Data Sufficiency - 51
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 440
Answer: B
Suppose the cost of each coat = x
Suppose sales price = y
=> Total cost = 20x and sales price = 20y
We are required to find the profit: 20(y-x).
From statement 1): It is given that 20(2y-x)=2400
Doesn't helps to find out 20(y-x) --- insufficient
From statement 2): It is given that 20(y+2-x) = 440,
=> 20(y-x) = 400 --- sufficient
Hence B
Friday, November 07, 2008
Data Sufficiency - 50
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 - C
From Statement 1): It is given that 25 percent of the projects at Company Z have 4 or more employees assigned to each project - but we donot know the percentage of projects who have employees less than 4 or in other words we do not have any information about the rest 75% projects ---- hence insufficient
From Statement 2): It is given that 35 percent of the projects at Company Z have 2 or fewer employees assigned to each project - but we donot know the percentage of projects who have employees more than 2 or in other words we do not have any information about the rest 65% projects---- hence insufficient
Taking both the statements together:
25 percent of the projects at Company Z have employees 4 , 5, 6..
35 percent of the projects at Company Z have employees 2, 1, 0
=> 40% of projects have 3 employees = > median value is 3
(1-35)employees -- (36-75)employees -- (76-100)employees
2 or less than 2 ---------3, 3, 3, ------------ 4 or more than 4
(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 - C
From Statement 1): It is given that 25 percent of the projects at Company Z have 4 or more employees assigned to each project - but we donot know the percentage of projects who have employees less than 4 or in other words we do not have any information about the rest 75% projects ---- hence insufficient
From Statement 2): It is given that 35 percent of the projects at Company Z have 2 or fewer employees assigned to each project - but we donot know the percentage of projects who have employees more than 2 or in other words we do not have any information about the rest 65% projects---- hence insufficient
Taking both the statements together:
25 percent of the projects at Company Z have employees 4 , 5, 6..
35 percent of the projects at Company Z have employees 2, 1, 0
=> 40% of projects have 3 employees = > median value is 3
(1-35)employees -- (36-75)employees -- (76-100)employees
2 or less than 2 ---------3, 3, 3, ------------ 4 or more than 4
Wednesday, June 04, 2008
Data Sufficiency - 49
Does the curve (x-a)^2 + (y-b)^2=16 intersect the y-axis ?
(1) a^2+b^2>16
(2) a=|b|+5
Answer: B
The given curve will intersect the y-axis when x=0
Thus we get a^2 + (y-b)^2 = 16
<=> a^2 + y^2 + b^2 - 2yb = 16
<=> y^2 - 2yb + a^2 + b^2 -16 = 0
In 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 <=16 --- hence insufficient
From statement (2): Given a = |b|+5
=> |b| is positive or zero.
=> a is atleast equal to 5 and value of a^2 is atleast 25.
But we know that a^2 <=16 ====> does not intersect the y axis ---- hence sufficient
Hence the answer B
(1) a^2+b^2>16
(2) a=|b|+5
Answer: B
The given curve will intersect the y-axis when x=0
Thus we get a^2 + (y-b)^2 = 16
<=> a^2 + y^2 + b^2 - 2yb = 16
<=> y^2 - 2yb + a^2 + b^2 -16 = 0
In 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 <=16 --- hence insufficient
From statement (2): Given a = |b|+5
=> |b| is positive or zero.
=> a is atleast equal to 5 and value of a^2 is atleast 25.
But we know that a^2 <=16 ====> does not intersect the y axis ---- hence sufficient
Hence the answer B
Thursday, May 01, 2008
Data Sufficiency - 48
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 1
Answer: E
From statement (1): |x-0|=|y-1|
x = y-1
x = 1-y ....hence insufficient
From 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 than 1
= -x+1-y less than 1 ....hence insufficient
Taking statements (1) and (2) together: still insufficient
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 1
Answer: E
From statement (1): |x-0|=|y-1|
x = y-1
x = 1-y ....hence insufficient
From 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 than 1
= -x+1-y less than 1 ....hence insufficient
Taking statements (1) and (2) together: still insufficient
Sunday, April 27, 2008
Data Sufficiency - 47
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: A
From statement (1): y=(1-m)x+(b+1) has the same slope as y=mx+b. (Parallel lines have same slope)
Thus 1-m = m
implies Slope of K=m=1/2 ---- Hence sufficient
From statement (2): just says line y=2x+3 is not parallel to K, these two lines can have any angle between them other than 0, 180, 360 degrees ---- hence insufficient
Hence answer A
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: A
From statement (1): y=(1-m)x+(b+1) has the same slope as y=mx+b. (Parallel lines have same slope)
Thus 1-m = m
implies Slope of K=m=1/2 ---- Hence sufficient
From statement (2): just says line y=2x+3 is not parallel to K, these two lines can have any angle between them other than 0, 180, 360 degrees ---- hence insufficient
Hence answer A
Data Sufficiency - 46
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 numbers
Answer: A
From 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 sufficient
From Statement (2): we know that a and b are both prime, this implies the greatest common factor will have to be 1 or if a = b could be the same prime number then the GCF would be a (=b). ...hence insufficient
NOTE: You cannot assume that a and b are different integers if the question stem does not states the same
(1) a and b share exactly one common factor
(2) a and b are both prime numbers
Answer: A
From 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 sufficient
From Statement (2): we know that a and b are both prime, this implies the greatest common factor will have to be 1 or if a = b could be the same prime number then the GCF would be a (=b). ...hence insufficient
NOTE: You cannot assume that a and b are different integers if the question stem does not states the same
Wednesday, March 19, 2008
Data Sufficiency - 45
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 cd
Answer: B
OE: 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 5 * 5 * 3 * 3. Notice that 225 is composed of a pair of 5's and a pair of 3's.
The problem states that x is a perfect square. The prime factors that build x are p, q, r, and s. In order for x to be a perfect square, these prime factors must come in pairs. This is possible if either of the following two cases hold:
Case One: The exponents a, b, c, and d are even. In the example 3^2 5^4 7^2 11^6, all the exponents are even so all the prime factors come in pairs.
Case Two: Any odd exponents are complemented by other odd exponents of the same prime. In the example 3^1 5^4 3^3 11^6, notice that 3^1 and 3^3 have odd exponents but they complement each other to create an even exponent (3^4), or "pairs" of 3's. Notice that this second case can only occur when p, q, r, and s are NOT distinct. (In this example, both p and r equal 3.)
Statement (1) tells us that 18 is a factor of both ab and cd. This does not give us any information about whether the exponents a, b, c, and d are even or not.
Statement (2) tells us that 4 is not a factor of ab and cd. This means that neither ab nor cd has two 2's as prime factors. From this, we can conclude that at least two of the exponents (a, b, c, and d) must be odd. As we know from Case 2 above, if paqbrcsd is a perfect square but the exponents are not all even, then the primes p, q, r and s must NOT be distinct.
The correct answer is B: Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
(1) 18 is a factor of ab and cd
(2) 4 is not a factor of ab and cd
Answer: B
OE: 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 5 * 5 * 3 * 3. Notice that 225 is composed of a pair of 5's and a pair of 3's.
The problem states that x is a perfect square. The prime factors that build x are p, q, r, and s. In order for x to be a perfect square, these prime factors must come in pairs. This is possible if either of the following two cases hold:
Case One: The exponents a, b, c, and d are even. In the example 3^2 5^4 7^2 11^6, all the exponents are even so all the prime factors come in pairs.
Case Two: Any odd exponents are complemented by other odd exponents of the same prime. In the example 3^1 5^4 3^3 11^6, notice that 3^1 and 3^3 have odd exponents but they complement each other to create an even exponent (3^4), or "pairs" of 3's. Notice that this second case can only occur when p, q, r, and s are NOT distinct. (In this example, both p and r equal 3.)
Statement (1) tells us that 18 is a factor of both ab and cd. This does not give us any information about whether the exponents a, b, c, and d are even or not.
Statement (2) tells us that 4 is not a factor of ab and cd. This means that neither ab nor cd has two 2's as prime factors. From this, we can conclude that at least two of the exponents (a, b, c, and d) must be odd. As we know from Case 2 above, if paqbrcsd is a perfect square but the exponents are not all even, then the primes p, q, r and s must NOT be distinct.
The correct answer is B: Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
Tuesday, February 05, 2008
Data Sufficiency - 44
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= 45
Answer: A
From 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 hypotenuse. Hence DC=5
(1) Angle C= 90
(2) Angle B= 45
Answer: A
From 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 hypotenuse. Hence DC=5
Sunday, February 03, 2008
Data Sufficiency - 43
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 TU
Answer: 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 of ST is equal to the length of line segment TU .. this implies angle TUS = angle TSU = q(say)
Hence p+p+angle QRS = 180 --- eq(1) and q+q+angle UTS = 180 --- eq(2)
Thus, p+q+x = 180
Now because angle RPT = 90, QRS+UTS= 90
adding eq(1) and eq(2) we get:
2p+2q+QRS+UTS = 360
2p+2q+90=360
p+q = 270/2 = 135
Now x = 180-p-q..hence the answer C
x = 180 - (p+q) = 180 - 135 = 45
Thursday, January 31, 2008
Data Sufficiency - 42
Is a-3b an even number?
1). b=3a+3
2). b-a is an odd number
Answer: C
From statement (1): Given that b=3a+3
Thus a-3b=a-3(3a+3) = -8a-9 which may be even, odd, integer, non-integer, rational etc ... Hence insufficient
From 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, non-integer, rational etc ..Hence insufficient
Taking statement (1) and (2) together: -8a-9=-2a-6k-3 for some integer k
or -6a=-6k+6=-6(k+1) implies a=k+1
Thus a is an integer, either odd or even
Now statement (2) tells us that b is also an integer and that exactly one of {a,b} is even
If a is even and b is odd, a-3b is odd
If b is even and a is odd a-3b is odd
Thus (1) and (2) combined tell us that a-3b is an odd number...hence sufficient
1). b=3a+3
2). b-a is an odd number
Answer: C
From statement (1): Given that b=3a+3
Thus a-3b=a-3(3a+3) = -8a-9 which may be even, odd, integer, non-integer, rational etc ... Hence insufficient
From 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, non-integer, rational etc ..Hence insufficient
Taking statement (1) and (2) together: -8a-9=-2a-6k-3 for some integer k
or -6a=-6k+6=-6(k+1) implies a=k+1
Thus a is an integer, either odd or even
Now statement (2) tells us that b is also an integer and that exactly one of {a,b} is even
If a is even and b is odd, a-3b is odd
If b is even and a is odd a-3b is odd
Thus (1) and (2) combined tell us that a-3b is an odd number...hence sufficient
Wednesday, January 30, 2008
Data Sufficiency - 41
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 5
Answer: A
From statement (1): Given that the slope of line AB is 3/4 and slope of line BC is -4/3. This implies that the product of slopes = -1. Hence AB perpendicular BC and B is a right angle. Thus AC is a diameter which implies ABC form a semi-circle.
Hence sufficient
From statement (2): Given that length of line AB is 12 and length of BC is 5. However this does not imply that ABC is a right angled triangle. We can draw number of different triangles with the same given two sides but with different third side.
Hence insufficient
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 5
Answer: A
From statement (1): Given that the slope of line AB is 3/4 and slope of line BC is -4/3. This implies that the product of slopes = -1. Hence AB perpendicular BC and B is a right angle. Thus AC is a diameter which implies ABC form a semi-circle.
Hence sufficient
From statement (2): Given that length of line AB is 12 and length of BC is 5. However this does not imply that ABC is a right angled triangle. We can draw number of different triangles with the same given two sides but with different third side.
Hence insufficient
Wednesday, January 23, 2008
Data Sufficiency - 40
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) = 0
Answer: C
Given 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 cannot determine that whether the line passes through (r,s) or not.
Hence insufficient
From statement (2): (4r-6-s)(3r+2-s) = 0 implies either (4r-6-s) = 0 or (3r+2-s) = 0
Now when (4r-6-s) = 0 ... we cannot determine that whether the line passes through (r,s) or not
When (3r+2-s) = 0..the line passes through (r,s)
Hence insufficient
Taking statement (1) and (2) together: (3r+2-s)(4r+9-s) = 0 and (4r-6-s)(3r+2-s) =0... We cannot have both 4r+9-s=0 and 4r-6-s=0 so it is (3r+2-s) = 0 ... only this equation makes both the equations to be 0
Hence sufficient
1) (3r + 2 - s)(4r + 9 - s) = 0
2) (4r - 6 - s)(3r + 2 - s) = 0
Answer: C
Given 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 cannot determine that whether the line passes through (r,s) or not.
Hence insufficient
From statement (2): (4r-6-s)(3r+2-s) = 0 implies either (4r-6-s) = 0 or (3r+2-s) = 0
Now when (4r-6-s) = 0 ... we cannot determine that whether the line passes through (r,s) or not
When (3r+2-s) = 0..the line passes through (r,s)
Hence insufficient
Taking statement (1) and (2) together: (3r+2-s)(4r+9-s) = 0 and (4r-6-s)(3r+2-s) =0... We cannot have both 4r+9-s=0 and 4r-6-s=0 so it is (3r+2-s) = 0 ... only this equation makes both the equations to be 0
Hence sufficient
Sunday, January 20, 2008
Data Sufficiency - 39
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: B
From statement (1): *triangle* can be both positive or negative as
n-0 = n
n+0 = n
Hence insufficient
From statement (2): *triangle* can only be negative in this case as
n-n = 0
Hence sufficient
(1) n *triangle* 0 = n for all integers n.
(2) n *triangle* n = 0 for all integers n.
Answer: B
From statement (1): *triangle* can be both positive or negative as
n-0 = n
n+0 = n
Hence insufficient
From statement (2): *triangle* can only be negative in this case as
n-n = 0
Hence sufficient
Monday, January 14, 2008
Problem Solving - 34
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?
Answer: B
Day 1 = 0.10
Day 2 = 0.20
Day 3 = 0.20*2 = 0.40
Thus on 4th day the total fine is: 0.10 + 0.20 + 0.40 = 0.70
A. $0.60
B. $0.70
C. $0.80
D. $0.90
E. $1.00
Answer: B
Day 1 = 0.10
Day 2 = 0.20
Day 3 = 0.20*2 = 0.40
Thus on 4th day the total fine is: 0.10 + 0.20 + 0.40 = 0.70
Friday, January 11, 2008
Data Sufficiency - 38
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 10
Answer: A
OE:
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 be a multiple of 4. As 2^7 is not a factor of q^4, the highest power of 2 that could be a factor of q^4 is 2^4.
Hence q^4 is not a multiple of 64=2^6......sufficient
From statement (2): Given that q^2 has 27 factors. Thus q^2 could be of the form
(i) a^26, or
(ii)b^2*c^8 or
(iii) a^2*b^2*c^2 where a b and c are distinct prime numbers.
Because q^2 has 7 factors less than 11, (i) is impossible.
As for (ii) 2^8*3^2 has exactly 7 factors under 11 (1,2,3,4,6,8,9), in which case q^4 would be a multiple of 64. 3^8*2*2 is not a possibility for q^2 (it only has 6 factors under 1: 1,2,3,4,6,9)
Regarding (iii) if q^2=2^2*3^2*5^2, q^2 would have 8 factors under 11- 1,2,3,4,5,6,9,10 and q^2=2^2*3^2*7^2 would have 7 factors under 11: 1,2,3,4,6,7,9) In this case, q^4 would not be a multiple of 64. Thus (2) is insufficient
hence the answer A
(1) q^4 is not a multiple of 128.
(2) q^2 has 27 factors, 7 of which are less than or equal to 10
Answer: A
OE:
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 be a multiple of 4. As 2^7 is not a factor of q^4, the highest power of 2 that could be a factor of q^4 is 2^4.
Hence q^4 is not a multiple of 64=2^6......sufficient
From statement (2): Given that q^2 has 27 factors. Thus q^2 could be of the form
(i) a^26, or
(ii)b^2*c^8 or
(iii) a^2*b^2*c^2 where a b and c are distinct prime numbers.
Because q^2 has 7 factors less than 11, (i) is impossible.
As for (ii) 2^8*3^2 has exactly 7 factors under 11 (1,2,3,4,6,8,9), in which case q^4 would be a multiple of 64. 3^8*2*2 is not a possibility for q^2 (it only has 6 factors under 1: 1,2,3,4,6,9)
Regarding (iii) if q^2=2^2*3^2*5^2, q^2 would have 8 factors under 11- 1,2,3,4,5,6,9,10 and q^2=2^2*3^2*7^2 would have 7 factors under 11: 1,2,3,4,6,7,9) In this case, q^4 would not be a multiple of 64. Thus (2) is insufficient
hence the answer A
Data Sufficiency - 37
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?
From statement (2): 10% Japanese studying students = 4% French studying students
10/100 study Japanese = 4/100 study French
25 study Japanese = 10 study French
Hence study French > study Japanese ... thus more students at the school study French than study Japanese....sufficient
Hence B
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: B
From statement (1):16 students study both French and Japanese, so 16/0.04=400 students study French. But we don't know how many the total number of students are so the number Japanese student can be at least 100 or more than 400....insufficientFrom statement (2): 10% Japanese studying students = 4% French studying students
10/100 study Japanese = 4/100 study French
25 study Japanese = 10 study French
Hence study French > study Japanese ... thus more students at the school study French than study Japanese....sufficient
Hence B
Data Sufficiency - 36
If set S consist of the numbers 1, 5, -2, 8, and n, is 0 less than n less than 7 ?
From 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 can also be n less than 0 ....insufficient
From statement (2): Median will be greater than 1 only if n is located above 1
Thus median will either be 5 if n greater than 5 or n if 1 less than n less than 5
Hence in both cases n greater than 1 but it can also be n greater than 7 ....insufficient
Taking statements (1) and (2) together: 1 less than n less than 5 which lies within the given interval 0 less than n less than 7 ...thus possible values for n are be 2, 3, or 4
Hence the answer C
1). the median of the numbers in S is less than 5.
2). the median of the numbers in S is greater than 1
From 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 can also be n less than 0 ....insufficient
From statement (2): Median will be greater than 1 only if n is located above 1
Thus median will either be 5 if n greater than 5 or n if 1 less than n less than 5
Hence in both cases n greater than 1 but it can also be n greater than 7 ....insufficient
Taking statements (1) and (2) together: 1 less than n less than 5 which lies within the given interval 0 less than n less than 7 ...thus possible values for n are be 2, 3, or 4
Hence the answer C
Tuesday, January 08, 2008
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