PI is a two digit number and PIE is a three digit number, where each

Question

PI is a two digit number and PIE is a three digit number, where each letter is a different digit from 0 to 9 (P ≠ 0). If  \sqrt{PI} + E = \sqrt{PIE} , what is the value of P + I + E ?

A. 10
B. 11
C. 12
D. 13
E. 16

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saurabh851 · Accepted Answer

Ans: E (16)

PI is a perfect square, possible values, 16, 25, 36, 49, 64, 81
PI^1/2 i.e., 4,5,6,7,8,9

E ranges from 0 to 9

PIE (3 digit number) is also perfect square with PI a perfect square, possible values
169, 256, 361 only
PIE^1/2 is 13, 16, 19..

Now, PI^1/2 + E = PIE^1/2
16^1/2 + 9 = 169^1/2
13 = 13

So, P+I+E = 1+6+9 = 16

Hope I am right...

nick1816 · Answer

\sqrt{PI} is a single digit number greater than or equal to 4. and E is also a single digit number.

Hence, Sum of them is less than or equal to 18

100 ≤ PIE ≤ 324

10 ≤ PI ≤ 32

Since first 2 digit of PIE is a perfect square, PI can be either 16 or 25.

Hence PIE can be 169 or 256

\sqrt{PIE} - \sqrt{PI} =E

\sqrt{256} - \sqrt{16} =12 (Not possible)

P+I+E = 1+6+9=25

yashikaaggarwal · Answer

PIE is a 3 digit perfect square whose digits are distinct from each other.
PIE = 169,196,256,289,324,361,529,576,625,729,784,841,961
Among these PI value can't exceed 9. Also PI is a perfect square.
So remaining values= 169,256,361

The value of P+I+E can be 16,13,9.
9 is not among option so we are left with 2 values..
Putting value in equation 
=> √PI + E = √PIE

PIE = 256
=> √25 + 6 = √256
=> 5+6 = 16
=> 11≠16 (incorrect)

PIE = 169
=> √16 + 9 = √169
=> 4+9 = 13
=> 13 = 13(correct)

Therefore Value of P+I+E = 1+6+9 = 16

Answer is E

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Adit_ · Answer

Only thing to note here being that the root value has to be something really small here. 
Once that is realise that it is all about potential pattern recognition of knowing squares of numbers. It makes the problem really simply.

We have 
16,25,36,49,64,81 all being possibilities.

Lets check 25.
We have 256 = 16^2 but 25 = 5^2 and E should be single digit. Ruled out.

36 is also possible with 361 = 19^2
But for E being single digit number, both the information cannot coincide. Ruled out.

49 is not possible as far as i know. Dont think there is any square where u add a digit to 49 and it becomes a square number.

64 again not possible, we only have 676 as a value close enough.

81 again not possible.

Well the answer is:

16  as we have 169 = root(16) + 9 and fits the solution perfectly.

1+6+9 = 16.

Answer:  Option E

PI is a two digit number and PIE is a three digit number, where each

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PI is a two digit number and PIE is a three digit number, where each

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