The numbers x and y are not integers. The value of x is closest to whi

Question

The numbers x and y are  not  integers. The value of x is closest to which integer?

(1) 4 is the integer that is closest to x + y.
(2) 1 is the integer that is closest to x - y

Bunuel · Answer

The numbers x and y are NOT integers. The value of x is closest to which integer?

(1) 4 is the integer that is closest to x+y --> \(3.5<x+y<4.5\). Not sufficient.
(2) 1 is the integer that is closest to x-y --> \(0.5<x-y<1.5\). Not sufficient.

(1)+(2) Sum above inequalities: \(4<2x<6\) --> \(2<x<3\) --> so \(x\) can be closer to 2 (for example if \(x=2.1\)) as well as to 3 (for example if \(x=2.9\)). Not sufficient.

Answer: E.

Check similar question: if-500-is-the-multiple-of-99421.html

Hope it helps.

Nayimoni · Answer

Numbers X and Y are not integers. the value of x is closest to which integer?

A. 4 is the integer that is closest to X+Y
B. 1 is the integer that is closest to X-Y

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Answer: I dont see any helpful rephrasing. Concepts tested are decimals.

1) so x + y equals 3.51 to 4.49 and x can be 0.52 and close to one or could be equal 3.48 and close to 3. Insuff. AD out

2) so x - y can be equal to 0.51 or 1.49 for example and x can be 1.01 and close to 1 or x could be 0.48 and x close to 0 Insuff B out

1+2) we know 3.51 < x + y < 4.49
 0.51 < x - y < 1.49

If we add both y cancels out and we get 4.02 < 2x < 5.98 and so 2.01 < x < 2.99 so x could be close to 2 or 3 Insuff

Answer is E.

siddhans · Answer

How do we know we need to take  3.5<x+y<4.5  or  3.5<=x+y<=4.5  ??????

KarishmaB · Answer

4 is the integer that is closest to x+y i.e. there is a single integer that is closest to (x+y)
If (x+y) = 3.5, which integer is closest to it? Both 3 and 4 are at equal distance i.e. they are both 0.5 away from (x+y). But then, we cannot say that 4 is the integer closest to x+y.
Hence, x+y must be greater than 3.5. It must also be less than 4.5 due to the same reason.

Note: 3.5 is rounded up to 4 instead of 3 only because we generally follow round up convention. If we follow 'round down' convention, 3.5 will be rounded off to 3. 
3.5 is equidistant from both 3 and 4.

Bunuel · Answer

Similar questions to practice: https://gmatclub.com/forum/if-500-is-the ... 99421.html https://gmatclub.com/forum/what-number-r ... 41970.html

BrentGMATPrepNow · Answer

Target question :    The value of x is closest to which integer?

Let's head straight to...........

Statements 1 and 2 combined    
There are several values of x and y that satisfy BOTH statements. Here are two: 
 Case a : x = 2.4 and y = 1.4. These values satisfy both statements. In this case, the answer to the target question is  2 is the closest integer to x 
 Case b : x = 2.6 and y = 1.4. These values satisfy both statements. In this case, the answer to the target question is  3 is the closest integer to x 
Since we cannot answer the  target question  with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent

Jsound996 · Answer

Here's a unique solution that you can solve this question in 20 secs (I think this is correct so experts please verify if it's a valid strategy)

Statement 1:
x+y is closest to 4. This means x+y = anywhere between 3.5 and 4.49999
 Statement 1 is Insufficient!

Statement 2:
x-y is closest to 1. This means x-y = anywhere between 0.5 and 1.49999
 Statement 2 is Insufficient!

Ok let's say that x+y = 4 and x-y = 1
If we multiple that statement, we should get (x+y)(x-y) =4
 X^2 - Y^2 = 4 
X can be both positive and negative numbers, and it can be any possible number too
 Both Statements combined is insufficient!

The Answer is E!

nimaki · Answer

(1) 4 is the integer that is closest to x + y.
   x + y  is less than our or greater than or equal to  3.5 .
 i.e  3.5 <= x + y < 4 
 It is   not sufficient  because we do not have enough information to settle on an value close to  x

(2) 1 is the integer that is closest to x - y
 The trouble here is double because we cannot know if   x-y < 1.5 or if x-y >= 0.5  .
 This concfusion means that this statement is  insufficient .

(1) & (2)  Let us be honest. No relationship can be made between statement (1) and (2). Therefore, none is sufficient   E

bumpbot · Answer

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