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What is the value of a?

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What is the value of a?  [#permalink]

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New post Updated on: 03 Aug 2014, 01:18
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What is the value of a?

Given \(a^2 + b^2\) = 116

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

Originally posted by sandeepk123 on 01 Aug 2014, 14:04.
Last edited by Gnpth on 03 Aug 2014, 01:18, edited 1 time in total.
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What is the value of a?  [#permalink]

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New post 03 Aug 2014, 01:18
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sandeepk123 wrote:
What is the value of a?

Given \(a^2 + b^2\) = 116

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


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.
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Re: What is the value of a?  [#permalink]

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New post 03 Aug 2014, 02:43
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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
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Re: What is the value of a?  [#permalink]

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New post 20 Mar 2018, 12:24
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)
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Re: What is the value of a?  [#permalink]

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New post 26 Mar 2018, 06:00

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
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Re: What is the value of a?   [#permalink] 26 Mar 2018, 06:00
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