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# If X and Y are positive integers such that X>Y, find X-Y.

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Director
Joined: 16 Jan 2019
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Location: India
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If X and Y are positive integers such that X>Y, find X-Y.  [#permalink]

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14 Jun 2019, 22:39
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Question Stats:

63% (02:15) correct 37% (01:26) wrong based on 62 sessions

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If $$X$$ and $$Y$$ are positive integers such that $$X>Y$$, find $$X-Y$$.

1. Greatest Common Factor of $$X$$ and $$Y$$ is 36

2. $$X+Y=288$$
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Re: If X and Y are positive integers such that X>Y, find X-Y.  [#permalink]

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14 Jun 2019, 22:53
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firas92 wrote:
If $$X$$ and $$Y$$ are positive integers such that $$X>Y$$, find $$X-Y$$.

1. Greatest Common Factor of $$X$$ and $$Y$$ is 36

2. $$X+Y=288$$

x,y>0; x>y all I

1. 36(a-b) = can't say. Insufficient.
x=36a, y=36b; where a and b are co primes.

2. x+y=288
287+1 or 286+2 both possible. Insufficient.

1+2 gives us
a+b= 8, a and b co primes
Both 1,7 and 3,5 possible. So E IMO
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If X and Y are positive integers such that X>Y, find X-Y.  [#permalink]

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14 Jun 2019, 22:57
1
firas92 wrote:
If $$X$$ and $$Y$$ are positive integers such that $$X>Y$$, find $$X-Y$$.

1. Greatest Common Factor of $$X$$ and $$Y$$ is 36

2. $$X+Y=288$$

Statement 1 - Insufficient as there are various numbers pairs having GCF as 36. such as 36*3 with 36*2; 36*2 and 36*5 that is 36 multiplied by two different prime numbers
Statement 2 - Insufficient and it does not help to arrive at unique values of X and Y

Combined : 288/36=8 will give the sum of two different prime numbers that are multiplied to the GCF of 36(As in statement 1). Still two one pair of prime numbers will satisfy which is 5 and 3, 7 and 1. IMO Option E
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Re: If X and Y are positive integers such that X>Y, find X-Y.  [#permalink]

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31 Mar 2020, 14:56
firas92 wrote:
If $$X$$ and $$Y$$ are positive integers such that $$X>Y$$, find $$X-Y$$.

1. Greatest Common Factor of $$X$$ and $$Y$$ is 36

2. $$X+Y=288$$

x,y=>0 and x>y, x>y

(1) insufic

gf(x,y)=36, x=36a and y=36b
many cases

(2) insufic

x+y=288

(1/2) insufic

x=288-y, 288-y-y>0, y<144;
0<y<144 and 144<x<288
y=36, x=288-36=252=36*7: gcf(x,y) is 36, valid
y=72=36*2, x=288-72=216=36*6: gcf(x,y) is not 36, invalid
y=108=36*3, x=288-108=180=36*5: gcf(x,y) is 36, valid
2 cases valid, thus insufic.

Ans (E)
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Re: If X and Y are positive integers such that X>Y, find X-Y.  [#permalink]

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31 Mar 2020, 16:03
firas92 wrote:
If $$X$$ and $$Y$$ are positive integers such that $$X>Y$$, find $$X-Y$$.

1. Greatest Common Factor of $$X$$ and $$Y$$ is 36

2. $$X+Y=288$$

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

Conditions 1) & 2)
If X = 252, Y = 36, then we have X-Y = 216.
If X = 180, Y = 108, then we have X-Y = 72.

Since both conditions together do not yield a unique solution, they are 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.
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Re: If X and Y are positive integers such that X>Y, find X-Y.   [#permalink] 31 Mar 2020, 16:03