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# If x and y are different prime numbers, is (50-x)/y an integer?

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Math Expert
Joined: 02 Aug 2009
Posts: 6956
If x and y are different prime numbers, is (50-x)/y an integer?  [#permalink]

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04 Feb 2018, 09:45
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3
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Difficulty:

95% (hard)

Question Stats:

32% (01:49) correct 68% (01:43) wrong based on 126 sessions

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If x and y are different prime numbers, is $$\frac{(50-x)}{y}$$ an integer?

(1) $$y=x+1$$.
(2) When y is divided by x, remainder is 1.

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Re: If x and y are different prime numbers, is (50-x)/y an integer?  [#permalink]

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04 Feb 2018, 09:53
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A

Not much info from question stem

Statement 1:

y=x+1

So x and y are consecutive prime numbers.

We know that the only consecutive prime numbers are 2 and 3. So x=2,y=3. Sufficient

Statement 2:

Many possibilities are there. If y=3, x=2 remainder is 1. Also for y=23, x=11 remainder is 1. Same for 5&2. Clearly insufficient.

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Re: If x and y are different prime numbers, is (50-x)/y an integer?  [#permalink]

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04 Feb 2018, 15:16
chetan2u wrote:
If x and y are different prime numbers, is $$\frac{(50-x)}{y}$$ an integer?

(1) $$y=x+1$$.
(2) When y is divided by x, remainder is 1.

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Since it's not entirely clear how to approach this question, we'll try picking numbers.
This is an Alternative approach.

(1) say x = 2 and y = 3, the smallest primes. Then 50 - 2 = 48 is divisible by 3.
Let's try challenging this by looking for another pair of numbers, such as... there is no other pair!
The only two prime numbers which are also consecutive are 2 and 3. Sufficient!

(2) x = 2 and y = 3 fulfill this and give us one answer of Yes. Let's try another pair.
Keeping x =2, we can choose y = 5. In this case 50 - 2 = 48 is not divisible by 5.

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Re: If x and y are different prime numbers, is (50-x)/y an integer?  [#permalink]

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14 Feb 2018, 07:40
chetan2u wrote:
If x and y are different prime numbers, is $$\frac{(50-x)}{y}$$ an integer?

(1) $$y=x+1$$.
(2) When y is divided by x, remainder is 1.

New question
source-self

chetan2u you are Christopher Nolan of questions, always a twist at the end.
Re: If x and y are different prime numbers, is (50-x)/y an integer? &nbs [#permalink] 14 Feb 2018, 07:40
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