GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 18 Jun 2019, 08:25 GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  If x and y are integers, is x a multiple of 5?

Author Message
TAGS:

Hide Tags

Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7465
GMAT 1: 760 Q51 V42 GPA: 3.82
If x and y are integers, is x a multiple of 5?  [#permalink]

Show Tags 00:00

Difficulty:   55% (hard)

Question Stats: 58% (01:55) correct 42% (01:13) wrong based on 54 sessions

HideShow timer Statistics

[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 $$5$$

_________________
Manager  S
Joined: 23 May 2017
Posts: 236
Concentration: Finance, Accounting
WE: Programming (Energy and Utilities)
Re: If x and y are integers, is x a multiple of 5?  [#permalink]

Show Tags

1
 x + y = 5k
(x = 0 ; y = 5 ) Answer = yes
(x = 1 ; y = 4 ) Answer = No

Hence  alone is not sufficient

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

Hence  alone is not sufficient

 + 

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
_________________
If you like the post, please award me Kudos!! It motivates me
Math Expert V
Joined: 02 Aug 2009
Posts: 7757
Re: If x and y are integers, is x a multiple of 5?  [#permalink]

Show Tags

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
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7465
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: If x and y are integers, is x a multiple of 5?  [#permalink]

Show Tags

=>

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.

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.
_________________ Re: If x and y are integers, is x a multiple of 5?   [#permalink] 09 Mar 2018, 00:19
Display posts from previous: Sort by

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