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Bunuel
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The sum of three digits in a number is 17, the sum of square of the di 06 Jun 2019, 02:21
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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15% (low)

Question Stats:

86% (02:09) correct 14% (02:20) wrong based on 76 sessions

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The sum of three digits in a number is 17, the sum of square of the digits is 109. If we subtract 495 from the number, the number is reversed. Find the number.

A. 683
B. 854
C. 863
D. 872
E. 953
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C
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The sum of three digits in a number is 17, the sum of square of the di 06 Jun 2019, 02:29
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Bunuel
The sum of three digits in a number is 17, the sum of square of the digits is 109. If we subtract 495 from the number, the number is reversed. Find the number.

A. 683
B. 854
C. 863
D. 872
E. 953
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using clue given in statement option C only gets reversed upon doing subtraction from 495
IMO C
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The sum of three digits in a number is 17, the sum of square of the di 06 Jun 2019, 02:32
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First I tried like a pro, name each digit and make equations
a+b+c=17
\(a^2+b^2+c^2=109\)

but then
Look at the answer choices
Only A and C satisfy the stem "the sum of square of the digits is 109"
Subtract each by 495 and find out which one satisfies "If we subtract 495 from the number, the number is reversed"

IMO
Ans C
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The sum of three digits in a number is 17, the sum of square of the di 06 Jun 2019, 02:37
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Here we can use hit and trial method to eliminate the options hence
Starting from the middle option ie option C 863 the sumof the digits is 17 and the sum of the square
A of the digits always equals to109 and also if we subtract 495 from the number we get 368 which reverse the number hence ans is
Option C
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The sum of three digits in a number is 17, the sum of square of the di 09 Jun 2019, 19:27
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Bunuel
The sum of three digits in a number is 17, the sum of square of the digits is 109. If we subtract 495 from the number, the number is reversed. Find the number.

A. 683
B. 854
C. 863
D. 872
E. 953
Show more


Although we can solve the problem algebraically, the best way is probably going through the answer choices to see which number satisfies all 3 criteria: 1) the sum of the digits of the number is 17, 2) the sum of the square of the digits is 109, and 3) the number reverses its digits when 495 is subtracted from it.

A. 683

1) 6 + 8 + 3 = 17 (Yes)

2) 6^2 + 8^2 + 3^2 = 36 + 64 + 9 = 109 (Yes)

3) 683 - 495 = 188 (No)

B. 854

1) 8 + 5 + 4 = 17 (Yes)

2) 8^2 + 5^2 + 4^2 = 64 + 25 + 16 = 105 (No)

C. 863

Since the 3 digits of this number are the same as those in A, we only need to check the last condition:

3) 863 - 495 = 368 (Yes)

Answer: C
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