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If A and B are positive integers, is B divisible by A?

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If A and B are positive integers, is B divisible by A?  [#permalink]

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New post 26 Apr 2016, 06:33
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

48% (02:00) correct 52% (01:37) wrong based on 139 sessions

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Re: If A and B are positive integers, is B divisible by A?  [#permalink]

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New post 26 Apr 2016, 08:59
Stmnt 1:
e.g 2*1/2 is an integer but 1/2 is not an integer
e.g 2*2/2 is an integer and 2/2 is also an integer
Different answers so Insufficient

Stmnt 2:
e.g 2^2/4 is an integer but 2/4 is not an integer
e.g 4^2/4 is an integer and 4/4 is also an integer
Different answers so Insufficient

Stmnt 1+2
e.g 2*2 /4 (2^2/4) is an integer but 2/4 is not an integer
e.g 2*4/4 or 4^2/4 is an integer and 4/4 is also an integer
Different answers so Insufficient

Ans E
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Re: If A and B are positive integers, is B divisible by A?  [#permalink]

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New post 13 Jan 2017, 04:40
Great Question.
We are told that A and B are positive integers and we are asked if if B/A is an integer or not.
Lets use some test cases here.

Statement 1->
2B/A is an integer.
Let A=1 and B=1 => 2B/A is an integer and B/A =1 which is an integer.
Let A=2 and B=1 => 2B/A is an integer and B/A=1/2 which is not an integer.
Hence not sufficient.
Statement 2->
B^2/A is an integer.
Let A=1 and B=1 => B^2/A is an integer and B/A=1 which is an integer.
Let A=4 and B=2 => B^2/A is an integer and B/A=1/2 which is not an integer.
Hence not sufficient.

Combing the two statements ->
Let A=1 and B=1 => B/A is an integer.
Let A=4 and B=2 => B/A is not an integer.
Hence not sufficient.
Hence E.

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Re: If A and B are positive integers, is B divisible by A?  [#permalink]

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New post 17 Jan 2017, 16:44
Bunuel wrote:
If A and B are positive integers, is B divisible by A?

(1) 2B/A is an integer.
(2) B^2/A is an integer.



From (1) 2B = k1*A => B = k1*A/2

If k1 is a non zero multiple of 2, then B is divisible by A. Since we do not know that information, (1) alone is insufficient.

From (2) B^2 = k2*A;

Can't say if B is a multiple of A or not. So (2) alone is insufficient.

Combining (1) & (2)

Substituting B = k1*A/2 in B^2 = k2*A

(k1^2*A^2)/4 = k2*A

k1^2 * A^2 = 4*k2*A

k1^2 * A = 4*k2

if A is equal to 1, then k1 is a multiple of 2, then answer would have been (C).

Since that is not the case here, answer is (E).
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If A and B are positive integers, is B divisible by A?  [#permalink]

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New post 01 Sep 2018, 02:25
niks18 chetan2u VeritasKarishma pushpitkc Bunuel ScottTargetTestPrep

What is incorrect in below approach?

Quote:
If A and B are positive integers, is B divisible by A?


A and B: Positive Integers, i.e. > 1
To find: if A is a factor or B or not?

Quote:
(1) 2B/A is an integer.

Can I say A is even from above.
Since I do not know value of B, insuff

Quote:
(2) B^2/A is an integer.

Can I say B is formed of same prime factors as A?
There are many prime factors greater than 1, insuff

Combining: we have only 2 as even prime no.
Suff.
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Re: If A and B are positive integers, is B divisible by A?  [#permalink]

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New post 01 Sep 2018, 05:57
adkikani wrote:
niks18 chetan2u VeritasKarishma pushpitkc Bunuel ScottTargetTestPrep

What is incorrect in below approach?

Quote:
If A and B are positive integers, is B divisible by A?


A and B: Positive Integers, i.e. > 1
To find: if A is a factor or B or not?

Quote:
(1) 2B/A is an integer.

Can I say A is even from above.
Since I do not know value of B, insuff

Quote:
(2) B^2/A is an integer.

Can I say B is formed of same prime factors as A?
There are many prime factors greater than 1, insuff

Combining: we have only 2 as even prime no.
Suff.
Hey adkikani

For statement 1

2*7/7 is an integer. But 7 is not an even number. That means A can be odd or even. Nothing is certain about it

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Re: If A and B are positive integers, is B divisible by A?   [#permalink] 01 Sep 2018, 05:57
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