Is √7ab an integer?

Question

Is  \sqrt{7ab}  an integer?

(1) a = 7
(2) b is equal to an integer raised to the third power.

Kudos for a correct  solution .

thembaseeker · Answer

Statement 1: talks nothing about variable b

Insufficient

Statement 2: talks nothing about variable a

Insufficient

Statement 1 and statement 2 together

when a=7 and b an integer raised to third power will not make the expression 7ab a perfect square.

Insufficient

Answer : E

GMATinsight · Answer

Question  : Is  \sqrt{7ab}  an integer?

Statement 1 : a = 7 
Case 1: @a=7 and b=1,  \sqrt{7ab} = \sqrt{7*7*1}=7  i.e. Integer
Case 2: @a=7 and b=2,  \sqrt{7ab} = \sqrt{7*7*2}=7\sqrt{2}  i.e. NOT an Integer
Hence,
NOT SUFFICIENT

Statement 2 : b is equal to an integer raised to the third power. 
Case 1: @a=1 and b=7^3,  \sqrt{7ab} = \sqrt{7*1*7^3}=7^2 = 49  i.e. Integer
Case 2: @a=2 and b=7^3,  \sqrt{7ab} = \sqrt{7*2*7^3}=7^2\sqrt{2}  i.e. NOT an Integer
Hence,
NOT SUFFICIENT

Combining the two statements  
Case 1: @a=7 and b=1^3,  \sqrt{7ab} = \sqrt{7*7*1^3}=7  i.e. Integer
Case 2: @a=7 and b=2^3,  \sqrt{7ab} = \sqrt{7*7*2^3}=7*2*\sqrt{2}  i.e. NOT an Integer
Hence,
NOT SUFFICIENT

Answer: option E

manishkhare · Answer

Option A provides value only for a .The figure changes from  \sqrt{7ab}  to  7\sqrt{(b)}  .Insufficient
Option B says  b= n^3  which is not sufficient to identify whether B is an integer .for n=7,  sqrt(7ab)  changes to  49sqrt(a)  .We do not know the value of A so it is insufficient .
for all other values of n, b is not an integer .

Combining both the options,  \sqrt{(7ab)}  can be written as 7 \sqrt{(b)}  .This is an integer only if b=1 .

Correct Answer =E.

Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION:

Question Type: Yes/No.  This question asks: “Is the square root of (7ab) an integer?”

Given information in the question stem or diagram: No important information is given in the question stem.

Statement 1: a = 7. This statement would change the question to: “Is the square root of 7 • 7 •b an integer?” This statement is not sufficient because while you know that 7^2 will still be an integer when the square root is taken, you do not know whether b is a perfect square. Not sufficient. Eliminate answers A and D.

Statement 2: b = an integer raised to the third power. This is also not sufficient. It says nothing about a. In order for the square root of 7ab to be an integer you need either a or b to have 7 as a factor and for the other variable to be a perfect square. This statement does not guarantee either of these. Eliminate choice B.

Together: Statement 1 brings the necessary 7 and takes care of that part. All that you need is for b to be a perfect square and then you would be sure that this square root is an integer. However, Statement 2 tells you that b is a perfect cube, not a perfect square. Many people will erroneously pick choice C at this point, thinking that this information proves that it could NEVER be an integer (which would give you a definitive “no” and be sufficient). However, there are many perfect cubes (1, 64, etc.) that are also perfect squares. Therefore together this information could result in either an integer or a non-integer and  the answer is E . Note: This is another great example of the importance of Playing Devil’s Advocate. Your gut reaction is that the statements together prove that it could never be an integer, but you need to consider all other ways it COULD be an integer. Considering the number 1 for the value of b is probably the easiest way to show that there is at least one way it could be an integer.

sdow · Answer

(1) a = 7
value of b is unknown, not possible to identify whether it is an integer or not, not sufficient
(2) b is equal to an integer raised to the third power.
a is unknown, not sufficient
Combined
value of b is unknown and not possible to take it out of the square root as it is raised to the third power, not sufficient

Is √7ab an integer?

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Is √7ab an integer?

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