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1/ Is x > y? (1) (x+y)/2 > 0 (2) (y-x)(y+x) > 0 2/ [#permalink]

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22 Jan 2005, 03:53

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A

B

C

D

E

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1/ Is x > y?
(1) (x+y)/2 > 0
(2) (y-x)(y+x) > 0

2/ One hundred students are taking both law and accounting. how many students are taking only accounting?
(1) 180 students are taking EITHER law OR accounting.
(2) 50 students are taking law but not accounting.

Directions:

A. If statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;

B. If statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;

C. If BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient;

D. If EACH statement ALONE is sufficient to answer the question asked;

E. If statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

1) gives us 180 = L + A
so we know L (U) A = 180 +100 = 280
not sufficient to know what is A

leaves us with choices B,C and E

2) gives us L= 50
if used alone
we won't be able to find [L (U) A] and [A] in tghe equation-
[L (U) A] = [L] + [A] + [L (I) A]
[L (U) A] = 50 + [A] + 100
not sufficient to know [A]...

but combining 1) and 2) gives us 50 + A = 180
i.e. A = 130

1. OA should be E.
y>x is not true.
if y=1, and x = -1 satisfies youranswer y>x.

from i, (x+y)/2>0 => x+y>0
but with these values, statement can not be true.
-1+1 is not greater than 0.

from ii, (y-x)(y+x) > 0
with the same values for x and y as in i,
(y-x)(y+x) > 0
(1+1)(1-1)>0

therefore OA should be E.

2/ One hundred students are taking both law and accounting. how many students are taking only accounting?
(1) 180 students are taking EITHER law OR accounting.
(2) 50 students are taking law but not accounting.

MA
1)
from statement 1, we get y>-x (1>-1) but we dont know if y is greater than X.

from statement 2 we get Y^2-x^2>0, i.e. y^2>x^2, but we still dont know if Y is greatern than +ve X or -ve X...so insufficient

taking the two together we realize that Y>-x but not greater than X, that is still unknown...so I think your answer is correct...

E its

2)
L+A=180, then also we know the overlap is 100, therefore
L(U)A=280= L + A - 100
280= 50+A -100

taking both statements is sufficient...C it is

MA wrote:

1. OA should be E. y>x is not true. if y=1, and x = -1 satisfies youranswer y>x.

from i, (x+y)/2>0 => x+y>0 but with these values, statement can not be true. -1+1 is not greater than 0.

from ii, (y-x)(y+x) > 0 with the same values for x and y as in i, (y-x)(y+x) > 0 (1+1)(1-1)>0

therefore OA should be E.

2/ One hundred students are taking both law and accounting. how many students are taking only accounting? (1) 180 students are taking EITHER law OR accounting. (2) 50 students are taking law but not accounting.

(1) (x+y)/2 > 0 .....x+y > 0......x > -y....for x = 1 and y = 1....satisfies....so x = y.....now x = 2 and y = 1.....2 > -1....so x > y....overall insuff

1. OA should be E. y>x is not true. if y=1, and x = -1 satisfies youranswer y>x.

from i, (x+y)/2>0 => x+y>0 but with these values, statement can not be true. -1+1 is not greater than 0.

from ii, (y-x)(y+x) > 0 with the same values for x and y as in i, (y-x)(y+x) > 0 (1+1)(1-1)>0

therefore OA should be E.

.

MA, ur example X = -1 and Y = 1...doesn't satisfy the statement 1....when u combine the 2 statements.....u actually know that...Y > X AND X > -Y...both of them has to be true and not just Y > X.....X = -1 and Y = 1 is not a valid example.

Last edited by banerjeea_98 on 23 Jan 2005, 12:07, edited 2 times in total.

When we take x = -1 and y = 1 as an example, we certainly cannot satisfy both the data given, i.e. (1) & (2). For a DS question, our job is to decide whether the data given in the statements are sufficient for answering the question.