If a and b are two numbers such that a*b = 10, is a an integer ?

Question

(1) 2a is an integer
(2) b is a not an integer

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QuantMadeEasy · Answer

a*b = 10
a = 10/b

(1) 2a is an integer 
Let 2a = z, where z is an integer
a = z/2
When z = 1, a = 1/2
When z = 2, a = 1
Insufficient

(2) b is a not an integer 
No information regarding a. Insufficient

Combining 
a = 10/b = z/2
hence, b = 20/z
When z = 3, b = 20/3, a = 3/2
When z = 40, b = 1/2, a = 20
Insufficient

IMO E

CEdward · Answer

Bunuel  I got confused with this one here
What is statement 2 saying?
b is a not an integer

carouselambra · Answer

IMO E

If a and b are two numbers such that a*b = 10, is a an integer ?

(1) 2a is an integer
Example :
a=1/2 , 2a will still be an integere
a=2, 2a is an integer
 (A) is not sufficient

(2) b is a not an integer
Example :
a=20, b=1/2 : A is an integer
a=3/2 , b=20/3 : A is not an integer
 (B) is not sufficient

Even after combining (A) and (B), we will not be able to arrive at the answer.

IMO (E)

Bunuel · Answer

Consider the following cases:

CASE 1: a = 20 and b = 1/2 (2a is an integer and b is a not an integer);
CASE 2: a = 3/2 and b = 20/3 (2a is an integer and b is a not an integer).

Answer: E.

Hope it helps.

TarunKumar1234 · Answer

Stat1: if 2a= integer, then a can be 1, 2,3,.. and 1/2, 3/2, 5/2...So, a can be an integer or not. Not sufficient.

Stat2: b is not integer. But, given a*b=10, it holds true, if a=3 and b=10/3, and a=3/10 and b=100/3. So, a can be an integer or not. Not sufficient.

Combining both stats, For a*b=10,
a= 3 and b=10/3 and
a=3/2 and b=20/3. So, a can be an integer or not. Not sufficient.

So, I think E.

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If a and b are two numbers such that a*b = 10, is a an integer ?

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