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

Question

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.

tinbilly · Answer

Many thanks, HSWKM!

However, for question no. 1, my choice is C.

(2) (y-x)(y+x) > 0
=> (y-x > 0) AND (y+x > 0)
OR (y-x < 0) AND (y+x < 0)

From (1) (x+y)/2 > 0 => x+y > 0

From (1) & (2) => y-x > 0 <=> y > x.

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

For question no. 2, please could you give your solution also?

Many thanks again.

bsarora · Answer

C, C
For the second one---

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   and   in tghe equation-
  =   +   +   
  = 50 +   + 100 
not sufficient to know  ...

but combining 1) and 2) gives us 50 + A = 180
i.e. A = 130

HongHu · Answer

C,C Wrong forum though, right?

MA · Answer

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. 


It is C.

FN · Answer

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

HongHu · Answer

It doesn't matter if y>x is true or not, as long as if we can determine whether y>x, then it is sufficient.

FN · Answer

I am confused...Ok tell me what you make of my explination??

banerjeea_98 · Answer

"C".

(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

(2) (y-x)(y+x) > 0 ......x = -2 ...y = -3.....satisfies ....x > y
 x = 1...y = 3.....satisfoes....y > x......so insuff

combine....

we know x+y > 0 from state 1....for statement 2 to hold true.....y-x > 0...so  y > x and x > -y  ....so ans is NO.....suff.

banerjeea_98 · Answer

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.

FN · Answer

I am consfused...(inequalities do that to me..LOL), all I can makeout is that Y>-x, but I cannot get how y>+x

statement ii) Y^2>x^2 which means either +,- ve y> +ve x or +,-ve y>-ve X combining the two statements leads us to believe that y>-veX?

banerjeea_98 · Answer

I edited my comment above...take a look....it will be clear...combined sol is Y > X AND X > -Y (OR Y > -X)...both has to hold true...not just Y > X

FN · Answer

banerjee....thanks! got it now...

MA · Answer

Banerjeea, 
i am not clear but i still think that E is the OA.

HongHu · Answer

1/ Is x > y? 
(1) (x+y)/2 > 0 
(2) (y-x)(y+x) > 0 

(1) =>x+y>0
(2) (y-x)(y+x)>0 Combine them, since y+x>0 =>y-x>0 therefore y>x
Sufficient

GMATPIPO · Answer

C & C 1. a) x + y > 0 ==> then x>y or x0 then two options: (+)(+) > 0 (y-x) > 0 and (y+x) >0 ..... (1) or (-)(-) > 0 (y-x) < 0 and (y+x) <0 ...... (2) from (1) y>x and (y+x) > 0 from (2) yx or y 0 that coincides with (b) (y+x) >0 when y>x then y>x (sufficient) C 2. C :wink:

tinbilly · Answer

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.

I surely choose C.

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

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