What is the value of a?

Question

Given  a^2 + b^2  = 116

1) a and b are integers
2) a < b

Gnpth · Answer

Statement-1 :

The Maximum values of a and b has to 10. As  11^2 =121.

So If b=4, a will be 10. If b=10, a will be 4. Two possible answers. So Insufficient.

Also both a and b can be negative as well. As any number raised to even power will be positive.

Eliminate A and D.

Statement-2:

If b=10, a has to be 4 or -4.

And if b=4, a will be 10 or -10. Similarly when b= -10 or -4.

No Perfect answers for a. Hence Insufficient.

Eliminate C as well. Since negative numbers are also integers. We will end up of having different values for a.

So Answer is E.

smyarga · Answer

Problem for 10 seconds:)
Just understand that you don't know signs of a and b, because they squared, and any statement doesn't help you to find their signs. So, you can't find the exact value of a. The correct answer is E.

Pairs of a and b:
-4, 10
-10, 4
4, 10
-10, -4

pushpitkc · Answer

What is the value of a?

Given  a^2 + b^2  = 116

1) a and b are integers
 4^2 + 10^2 = 116 
a could take values of either 4 or 10  (Insufficient)

2) a < b
Case 1: a = 4, b = 10
Case 2: a = -4, b = 10
Here a could be +4 or -4 because  -4^2 = 4^2 =16   (Insufficient)

On combining the information from both the statements,
a could take be -4 or 4.  (Insufficient - Option E)

EgmatQuantExpert · Answer

Solution

We are given:

•  a^2+b^2 = 116 
•  10^2+4^2 = 116 , the possible values of  a  and  b  are:
 o  a= 10, b=4 
o  a= 10, b= -4 
o  a= -10, b=4 
o  a= 10, b=-4 
o  a= 4, b= 10 
o  a= 4, b= -10 
o  a=-4, b=10 
o  a= -4, b= -10

Statement -1 : “  a  and  b  are integers ”

In all the above cases,  a  and  b  are integer.

We cannot arrive at a unique value of  a .
Hence,  Statement 1 is not sufficient to answer the question .

Statement -2:  “ a < b ”

The value of  a  is less than  b  for various cases.
 •  a= -10, b=4 
•  a= 4, b= 10 
•  a=-4, b=10

We cannot arrive at a unique value of  a .
Hence,  Statement 2 is not sufficient to answer the question.

Combining both the statements together:

After combining the statements,  a =  4 or -4 or -10 .
Hence,  we can not answer the question even after combining both the statements.

Answer: E

ManifestDreamMBA · Answer

a^2 + b^2  = 116

Statement 1
a and b are integers
The integers should be less than 11 as 11^2 = 121, and 116< 121
Squares could be 0,1,4,9,16,25,36,49,64,81,100
a^2 could be 16 and b^2 could be 100 or vice versa
a, b could be (4,10), (-4,10), (-4,-10), (4,-10), (10,4), (10,-4), (-10,4), (-10,-4)
Insufficient

Statment 2
a<b
But we don't know if a and b are integers
Insufficient

Together we have a, b could be (4,10), (-4,10), (-10,4), (-10,-4)
Insufficient

Answer E

What is the value of a?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards