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If x and y are integers, is x a multiple of 5?

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If x and y are integers, is x a multiple of 5?  [#permalink]

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New post 07 Mar 2018, 03:38
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A
B
C
D
E

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Question Stats:

61% (01:58) correct 39% (01:17) wrong based on 51 sessions

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[GMAT math practice question]

If \(x\) and \(y\) are integers, is \(x\) a multiple of \(5\)?

1) \(x+y\) is a multiple of \(5\)
2) \(x+2y\) is a multiple of \(5\)

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Re: If x and y are integers, is x a multiple of 5?  [#permalink]

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New post 07 Mar 2018, 04:10
1
[1] x + y = 5k
(x = 0 ; y = 5 ) Answer = yes
(x = 1 ; y = 4 ) Answer = No

Hence [1] alone is not sufficient

[2] x + 2y = 5m
( x = 0 ; y = 5 ) Answer = yes
( x = 4 ; y = 3) Answer = No

Hence [2] alone is not sufficient

[1] + [2]

x + y + y = 5m
5k + y = 5m
so y is a multiple of 5

so from statement 1 : x + y = 5k ; if y is a multiple of 5 , then x must also be multiple of 5
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Re: If x and y are integers, is x a multiple of 5?  [#permalink]

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New post 07 Mar 2018, 04:50
MathRevolution wrote:
[GMAT math practice question]

If \(x\) and \(y\) are integers, is \(x\) a multiple of \(5\)?

1) \(x+y\) is a multiple of \(5\)
2) \(x+2y\) is a multiple of \(5\)



Clearly statement 1 and II are insufficient...
1) x+y is a multiple of 5..
Both x and y are multiple of 5..
5+15 is MULTIPLE of 5..
Both x and y are not a multiple of 5
Insufficient

2) x+2y is a multiple of 5..
Same as above..
Insuff

Combined..
Multiple of 5-multiple of 5 has to be a MULTIPLE of 5..
So x+2y-(x+y) should be a MULTIPLE of 5..
x+2y-x-y=y is a multiple of 5..
So x also has to be a MULTIPLE of 5 as seen above..
Sufficient

C
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: If x and y are integers, is x a multiple of 5?  [#permalink]

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New post 09 Mar 2018, 00:19
=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 2 variables (\(x\) and \(y\)) and 0 equations, C is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables with the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2):
\(x = 2(x+y) – (x+2y)\) is a multiple of \(5\) since \(2(x+y)\) and \((x+2y)\) are multiples of \(5\).
Thus, both conditions 1) & 2) together are sufficient.

Since this question is an integer question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.

Condition 1)
If \(x = 5\) and \(y = 5\), \(x\) is a multiple of \(5\), and the answer is ‘yes’.
If \(x = 2\) and \(y = 3\), \(x\) is not a multiple of \(5\), and the answer is ‘no’.
Thus condition 1) is not sufficient.

Condition 2)
If \(x = 5\) and \(y = 5\), \(x\) is a multiple of \(5\), and the answer is ‘yes’.
If \(x = 1\) and \(y = 2\), \(x\) is not a multiple of \(5\), and the answer is ‘no’.
Thus condition 2) is not sufficient.

Therefore, the answer is C.

Answer: C

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
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Re: If x and y are integers, is x a multiple of 5? &nbs [#permalink] 09 Mar 2018, 00:19
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