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TAGS: Moderator  Joined: 18 Apr 2015
Posts: 5898
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Kudos [?]: 1156  , given: 5481

If x and y are integers, then [#permalink]
1
KUDOS
Expert's post 00:00

Question Stats: 78% (01:17) correct 21% (01:40) wrong based on 28 sessions

If x and y are integers, then $$\frac{(x) (x + 1) (x + 2)}{2*3*5^y}$$ must be an integer if which of the following is true ?

A. x is even.

B. x is odd.

C. x is divisible by three.

D. y is even.

E. y is equal to zero.
[Reveal] Spoiler: OA

_________________ Intern Joined: 08 Dec 2017
Posts: 40
Followers: 1

Kudos [?]: 39  , given: 70

Re: If x and y are integers, then [#permalink]
1
KUDOS
In here, the numerator is the product of consecutive integers. So it would be divisible by 2 and 3. If y=0, then the given fraction will be an integer.
So the answer is E. Director  Joined: 07 Jan 2018
Posts: 604
Followers: 7

Kudos [?]: 546  , given: 88

Re: If x and y are integers, then [#permalink]
1
KUDOS
take $$y = 10$$ and for consecutive integers take some small numbers such as $$1, 2, 3 or 2, 3, 4 or 3, 4, 5$$
doing so will invalidate all of the options from A to D because non of the final result will be an integer
Leaving only E for ans
_________________

This is my response to the question and may be incorrect. Feel free to rectify any mistakes

Manager Joined: 29 Nov 2017
Posts: 190
Location: United States
GRE 1: Q142 V146 WE: Information Technology (Computer Software)
Followers: 0

Kudos [?]: 78 , given: 99

Re: If x and y are integers, then [#permalink]
amorphous wrote:
take $$y = 10$$ and for consecutive integers take some small numbers such as $$1, 2, 3 or 2, 3, 4 or 3, 4, 5$$
doing so will invalidate all of the options from A to D because non of the final result will be an integer
Leaving only E for ans Director  Joined: 07 Jan 2018
Posts: 604
Followers: 7

Kudos [?]: 546  , given: 88

Re: If x and y are integers, then [#permalink]
2
KUDOS
When we assume $$x, x+1$$ and $$x+2$$ as $$1,2,3$$ or $$2,3,4$$ or $$3,4,5$$
while replacing these values in the given expression we can cancel of digits.
In the first two cases $$2$$ and $$3$$ are cancelled off and we are left with $$\frac{1}{5^y}$$ and $$\frac{4}{5^y}$$
Take $$y$$ as a large number because we are working with a $$must be$$ type questions so the ans must be valid in all circumstances.
In both the case the ans will not be an integer unless y = 0.
For the final case $$3$$ gets cancelled of and we are left with $$\frac{10}{5^y}$$. For this we can still get an integer if $$y$$= odd i.e $$1$$ but it is not the case always as we have found out earlier.
therefore best way to answer this question is to chose a large value for $$y$$ and make sure we can eliminate as many options as possible.
_________________

This is my response to the question and may be incorrect. Feel free to rectify any mistakes

Intern Joined: 14 Jun 2018
Posts: 36
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Kudos [?]: 7 , given: 100

Re: If x and y are integers, then [#permalink]
amorphous wrote:
When we assume $$x, x+1$$ and $$x+2$$ as $$1,2,3$$ or $$2,3,4$$ or $$3,4,5$$
while replacing these values in the given expression we can cancel of digits.
In the first two cases $$2$$ and $$3$$ are cancelled off and we are left with $$\frac{1}{5^y}$$ and $$\frac{4}{5^y}$$
Take $$y$$ as a large number because we are working with a $$must be$$ type questions so the ans must be valid in all circumstances.
In both the case the ans will not be an integer unless y = 0.
For the final case $$3$$ gets cancelled of and we are left with $$\frac{10}{5^y}$$. For this we can still get an integer if $$y$$= odd i.e $$1$$ but it is not the case always as we have found out earlier.
therefore best way to answer this question is to chose a large value for $$y$$ and make sure we can eliminate as many options as possible.

So for this types of questions, there is no general rule? It's trial and error approach?
Moderator  Joined: 18 Apr 2015
Posts: 5898
Followers: 96

Kudos [?]: 1156 , given: 5481

Re: If x and y are integers, then [#permalink]
Expert's post
Sometimes the only way to tackle a question is trial and error, even though is time consuming.

However, amorphous above provided a pretty fast and elegant solution to you

Quote:
take $$y = 10$$ and for consecutive integers take some small numbers such as $$1, 2, 3 or 2, 3, 4 or 3, 4, 5$$
doing so will invalidate all of the options from A to D because non of the final result will be an integer
Leaving the only E for ans

To speed up, even more, the process you could think about two things:

- first off: when a question asks you "which of the following" start always from the bottom of the answer choices. More often than not the correct answer is from the bottom-up:
- secondly: the numerator of the fraction is 3 consecutive integers.

if x is even = 2 AND y= 0, which means that $$5^0 = 1$$ then you do have

$$\frac{2*3*4}{2*3*1}$$

2 and 3 cancel out and you do have $$\frac{4}{1} = 4$$.

Now, the question has only one correct answer and it is also a must be true question. As such, E must be the correct answer without bothering you to check the others.

Hope now is clear to you.

Regards
_________________ Re: If x and y are integers, then   [#permalink] 07 Jul 2018, 11:13
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