CAT 2005 — QA Question 1
Remainders BasicsEasy
If x = (163 + 173 + 183 + 193), then x divided by 70 leaves a remainder of
Answer & solution
0
- B
1
- C
69
- D
35
Solution
x = 163 + 173 + 183 + 193
= (163 + 193) + (173 + 183)
= (16 + 19)(162 − 16 × 19 + 192) + (17 + 18)(172 − 17 × 18 + 182)
35 × (an odd number) + 35 × (another odd number) = 35 × (an even number)
= 35 × (2k) … (k is a positive integer)
∴ x = 70k
∴ x is divisible by 70.
Remainder when x is divided by 70 = 0
Hence, option (a).