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

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ezinis
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The numbers x and y are not integers. The value of x is closest to whi [#permalink] New post   Updated on: 22 Oct 2019, 08:24
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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
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E

Originally posted by ezinis on 04 Jan 2011, 13:52.
Last edited by Bunuel on 22 Oct 2019, 08:24, edited 2 times in total.
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Re: The numbers x and y are not integers. The value of x is closest to whi [#permalink] New post   04 Jan 2011, 14:05
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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.
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Re: The numbers x and y are not integers. The value of x is closest to whi [#permalink] New post   04 May 2011, 10:52
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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

---

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.
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Re: The numbers x and y are not integers. The value of x is closest to whi [#permalink] New post   21 Nov 2011, 18:50
Bunuel wrote:
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.

How do we know we need to take \(3.5<x+y<4.5\) or \(3.5<=x+y<=4.5\) ??????
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Re: The numbers x and y are not integers. The value of x is closest to whi [#permalink] New post   24 Nov 2011, 22:35
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siddhans wrote:
How do we know we need to take \(3.5<x+y<4.5\) or \(3.5<=x+y<=4.5\) ??????


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.
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The numbers x and y are not integers. The value of x is closest to whi [#permalink] New post   27 Oct 2014, 02:20
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Similar questions to practice:
https://gmatclub.com/forum/if-500-is-the ... 99421.html
https://gmatclub.com/forum/what-number-r ... 41970.html
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Re: The numbers x and y are not integers. The value of x is closest to whi [#permalink] New post   05 Sep 2018, 07:51
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ezinis wrote:
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


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
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Re: The numbers x and y are not integers. The value of x is closest to whi [#permalink] New post   06 Aug 2020, 00:22
ezinis wrote:
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


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!

Show Spoiler
The Answer is E!
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The numbers x and y are not integers. The value of x is closest to whi [#permalink] New post   02 Oct 2022, 05:11
(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.[/color]

(1) & (2) Let us be honest. No relationship can be made between statement (1) and (2). Therefore, none is sufficient E
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Re: The numbers x and y are not integers. The value of x is closest to whi [#permalink] New post   17 Nov 2023, 00:15
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Re: The numbers x and y are not integers. The value of x is closest to whi [#permalink]
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