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

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

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New post 04 Feb 2018, 09:45
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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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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 different prime numbers, is (50-x)/y an integer?  [#permalink]

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New post 04 Feb 2018, 09:53
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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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New post 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.

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

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New post 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.


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chetan2u you are Christopher Nolan of questions, always a twist at the end.
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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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If x and y are different prime numbers, is (50-x)/y an integer?

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