A positive integer x leaves a remainder of 1 when divided by 2, 3, and

Question

A positive integer x leaves a remainder of 1 when divided by 2, 3, and 4, and is divisible by 5. If x is the least possible value, what is the sum of the digits in x?

A. 6
B. 7
C. 8
D. 3
E. 1

Praveena_10 · Answer

The numbers leave same remainder if divisible by 4 and 2. So, X should be the number which leaves remainder 1 when divided by LCM of 4 and 3 i.e, 12.

By this X would be 25 least X as it should be divisible by 5 and leaves the remainder 1 when it divided by 24 which is a multiple of 12.

sujoykrdatta · Answer

Lcm of 2,3,4 is 12
So the number is 1 + a multiple of 12 ie 12m + 1
Since we need it to be divisible by 5, m=2 and the number is 25

Sum of digits is 7

zhangwma · Answer

Ended up using the below method, which isn't the fastest, but did get me to the right answer on my first attempt.

1. Using answer choices, I eliminated a) 1 because there are no positive integers that can sum to obtain 1 (keyword being positive and not non-negative, which could have added 0 into the mix as a possibility).

2. Starting with d) 3, I listed the possible positive addends that would sum to the answer choices and selected d) because it had the fewest (i.e., fastest to calculate). 1 + 2 are the only positive addends, so x could be 12 or 21, both of which aren't divisible by 5.

3. With answer c) 8, I listed: 1+7 (17 and 71 not divisible by 5), 2+6 (26 and 62 not divisible by 5), 3+5. Knowing 35 is divisible by 5, I started there and divided by the divisor 4 to see if the remainder was 1 (it's not, R = 3). Knowing 53 could not work (not divisible by 5), I moved to answer b.

4. b) 7 is possible from 1+6 (16 and 61 not divisible by 5), 2+5 (started with 25). 
25/4 = 6 R 1 --> works
25/3 = 8 R 1 --> works
25/2 = 12 R 1 --> works

Answer b) 7.

A positive integer x leaves a remainder of 1 when divided by 2, 3, and

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A positive integer x leaves a remainder of 1 when divided by 2, 3, and

Prep Toolkit

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

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