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23 Apr 2018, 01:15
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
86% (01:09) correct
14%
(01:46)
wrong
based on 90
sessions
History
Date
Time
Result
Not Attempted Yet
The units digit of a 3-digit number is 1/3 times the hundreds digit and twice the tens digit. What is the number?
(A) 126
(B) 216
(C) 312
(D) 612
(E) 621
(A) 126
(B) 216
(C) 312
(D) 612
(E) 621
23 Apr 2018, 04:46
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Bunuel
The unit digit must be even because it is twice the tenth digit. The unit digit must be 2 because any other even number cannot satisfy the condition of the unit digit being 1/3 of the hundreds digit.
unit digit = 2
tens digit = 1 (half of the unit digit)
hundreds digit = 6 (thrice the unit digit).
Alternative method is by testing the options. Only option D satisfy the conditions in the question.
Hence option D = 612 is the answer.
23 Apr 2018, 06:56
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Solution
Given
- • The number is having 3 digits
• Unit digit = 1/3 * hundred digit
• Unit digit = 2 * tenth digit
To find
- • The value of the 3-digit number
Approach and Working:
Assuming the 3-digit number as abc, all of a, b, and c are individually single digit integers.
Also, c = \(\frac{1}{3}\) * a and c = 2 * b, which implies b = \(\frac{1}{2}\) * c
As, c = = 1/3 * a, a must be a single digit multiple of 3.
Or, a can be either of 3, 6, or 9.
- • If a = 3, then c = \(\frac{1}{3}\) * 3 = 1, and b = \(\frac{1}{2}\) * 1 = \(\frac{1}{2}\)
- • This is not possible as b can’t be a fraction
• If a = 6, then c = \(\frac{1}{3}\) * 6 = 2, and b = \(\frac{1}{2}\) * 2 = 1
- • Therefore, abc = 612
• If a = 9, then c = \(\frac{1}{3}\) * 9 = 3, and b = \(\frac{1}{2}\) * 3 = \(\frac{3}{2}\)
- • This is not possible as b can’t be a fraction
The correct answer is Option D
Answer: D
