If a and b are positive integers, is a/b an integer?

Question

(1) b is a multiple of a 
(2) b > 1

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yashikaaggarwal · Answer

If a and b are positive integers, is a/b an integer?

(1) b is a multiple of a
Let say A = 3
B can be 3,6,9......

Case 1: A=B=3
A/B = 1 {integer}

Case 2: A= 3 and B = 6
A/B = 3/6 = 0.5 {Non-Integer}
(Not sufficient)

(2) b > 1
No information about A (Not Sufficient)

1 & 2 together: Still not Sufficient

IMO E

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BrentGMATPrepNow · Answer

Given : a and b are positive integers

Target question :    Is a/b an integer?

When I SCAN the two statements, they both feel insufficient, AND I’m pretty sure I can identify some cases with conflicting answers to the  target question . So, I’m going to head straight to……

Statements 1 and 2 combined    
There are several values of a and b that satisfy BOTH statements. Here are two: 
 Case a : a = 2 and b = 2 (aside: this satisfies the condition that  b is a multiple of a ). In this case, a/b = 2/2 = 1. So, the answer to the target question is  YES, a/b is an integer 
 Case b : a = 2 and b = 6. In this case, a/b = 2/6 = 1/3. So, the answer to the target question is  NO, a/b is not an integer 
Since we can't answer the  target question  with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent

NikitaVChoudhary · Answer

We can rephrase question as is a divisible by b?

1. b=na n is a positive integer

if n=1 then a is divisible by b
if n>1 the no

Not sufficient

2. b>1, this choice does not talk about a

Not sufficient

1+2

b=na>1 but still, we can't find out the values of a and b therefore not sufficient

hence E

Kinshook · Answer

Asked: If a and b are positive integers, is a/b an integer?

(1) b is a multiple of a 
b = ka; a/b = 1/k 
If k=1; YES; Otherwise NO
NOT SUFFICIENT

(2) b > 1
No information is given about a
NOT SUFFICIENT

(1) + (2) 
(1) b is a multiple of a 
(2) b > 1
b = ka > 1
a/b = 1/k 
If a=b; or k = 1; YES, otherwise NO
NOT SUFFICIENT

IMO E

GMATinsight · Answer

Question: Is a/b and Integer?

Statement 1 : b is a multiple of a

CONCEPT : The multiple of any number x ≥ x

If a = 4 and b = 4 then a/b is an Integer
If a = 4 and b = 8 then a/b is NOT an Integer

NOT SUFFICIENT

Statement 2 : b > 1

No information about a hence

NOT SUFFICIENT

COmbining the statements  
i.e. b is a multiple of a and b > 1

If a = 4 and b = 4 then a/b is an Integer
If a = 4 and b = 8 then a/b is NOT an Integer

NOT SUFFICIENT

Answer: Option E

If a and b are positive integers, is a/b an integer?

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