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If x and y are prime numbers, and a and b are positive integers, is x/

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Bunuel
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If x and y are prime numbers, and a and b are positive integers, is x/ [#permalink] New post   30 Jun 2020, 01:56
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If x and y are prime numbers, and a and b are positive integers, is x/a = y/b?

(1) x = 2 and y =7
(2) a = x^2 and b = xy
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B
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If x and y are prime numbers, and a and b are positive integers, is x/ [#permalink] New post   Updated on: 01 Jul 2020, 00:47
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IMO B

x, y ->prime numbers,
a, b ->positive integers,

Is x/a = y/b?

(1) x = 2 and y =7

If a=2 & b=7 ; x/a = y/b
But, if a=3 & b=5 ; x/a ≠ y/b
Not Sufficient.

(2) a = x^2 and b = xy
a = x^2 => a/x = x => x/a = 1/x
& b/y = x => y/b=1/x
Since, for x≠0, 1/x = 1/x => x/a = y/b
Therefore, x/a = y/b
Sufficient

Originally posted by MayankSingh on 30 Jun 2020, 03:57.
Last edited by MayankSingh on 01 Jul 2020, 00:47, edited 1 time in total.
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Re: If x and y are prime numbers, and a and b are positive integers, is x/ [#permalink] New post   30 Jun 2020, 04:03
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optio1: a and b can be any value
not sufficient

2. x/a= y/b
x/x^2 = y/xy
Sufficient

hence B
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Re: If x and y are prime numbers, and a and b are positive integers, is x/ [#permalink] New post   30 Jun 2020, 06:46
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IMO B

Stmt 1
Doesnot give anything about a and b .
Insuff

Stmt 2
a and b are given which results in 1/x = 1/x.
Yes to our question
Suff.
Suff

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Re: If x and y are prime numbers, and a and b are positive integers, is x/ [#permalink] New post   30 Jun 2020, 07:26
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From statement 1:

x = 2 and y = 7;
And a and b are positive integers which gives number of possibilities
Say a = 2 and b = 7,
Therefore the equality x/a = y/b holds true;
Now, if a = 1 and b = 14,
The equality x/a = y/b fails;
Hence insufficient.

From statement 2:

a = x.x and b = x.y;
Putting directly into the equation x/(x.x) = y/(x.y)
Which will always give x\(^-^1\) on both sides and holds true for any value of x.
Hence, Sufficient.

IMO ans is B.
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Re: If x and y are prime numbers, and a and b are positive integers, is x/ [#permalink] New post   30 Jun 2020, 08:32
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Ans -B
We need to prove x/y = a/b

Statement 1 - only gives values of x and Y, not sufficient, as a and b can be anything

Statement 2- with given info
x/y=a/b= x2/xy = x/y, sufficient Info.
Note- negative integers are not prime and a,b are +I given

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Re: If x and y are prime numbers, and a and b are positive integers, is x/ [#permalink] New post   30 Jun 2020, 21:53
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If x and y are prime numbers, and a and b are positive integers, is x/a = y/b?

(1) x = 2 and y =7
(2) a = x^2 and b = xy

1) we dont know the value of a and b
insufficient

2) x/x^2 = y/xy
1/x = 1/x
sufficient

Ans B
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Re: If x and y are prime numbers, and a and b are positive integers, is x/ [#permalink] New post   30 Jun 2020, 02:40
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Explanation:

Statement 1: x = 2 and y =7
2/a = 7/b

Don't know the value of a,b.
Not sufficient.

Statement 2: a = x^2 and b = xy
x/x^2 = y / xy
1 = 1

Sufficient

IMO-B
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Re: If x and y are prime numbers, and a and b are positive integers, is x/ [#permalink] New post   30 Jun 2020, 02:46
Given: If x and y are prime numbers, and a and b are positive integers,

To find: is x/a = y/b?

Solution:
(1) x = 2 and y =7
No value given for a and b, they could be 2 & 7 or any other pair. (Insufficient)

(2) a = x^2 and b = xy
Putting value in equation
X/X^2 = Y/XY
1/X = 1/X
(Sufficient)

Answer is B

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Re: If x and y are prime numbers, and a and b are positive integers, is x/ [#permalink] New post   30 Jun 2020, 06:28
Quote:
If x and y are prime numbers, and a and b are positive integers, is x/a = y/b?

(1) x = 2 and y =7
(2) a = x^2 and b = xy


Statement 1 : We don't get the value of a and b.
x/a may be equal to y/b or not.
Hence, insufficient.

Statement 2 :
\(\frac{x}{a} = \frac{y}{b}\)
From statement 2 we get, a = x^2 and b = xy
=> \(\frac{x}{x^2} = \frac{y}{xy}\)
Cross multiplying we get
=>\( x^2y = x^2y\)
Hence, sufficient.
Thus. OA is B
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Re: If x and y are prime numbers, and a and b are positive integers, is x/ [#permalink] New post   30 Jun 2020, 11:46
Answer: B
Prime number are positive numbers.
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Re: If x and y are prime numbers, and a and b are positive integers, is x/ [#permalink] New post   30 Jun 2020, 22:20
IMO-B
Given
X and y are prime number
And x/a=y/b ?

Statement-1
Given
X=2
Y=7
Here value of a and b is not certain

Insufficient

Statement-2
Assume x=2and y= 5
Then
a=x^2 =4
b=xy =10
X/a=y/b
1/2=1/2
Sufficient

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Re: If x and y are prime numbers, and a and b are positive integers, is x/ [#permalink]
30 Jun 2020, 22:20
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