gmatophobia
PS Question 1 - Nov 16
N is a positive 3-digit integer in which all three digits have the same value. The product 53N is a 5-digit integer comprised of five of the following six digits: 1, 2, 4, 6, 7, 9
Which of the following digits is NOT in the product 53N?
A) 1
B) 2
C) 4
D) 6
E) 7
Source: GMATPrepNow | Difficulty: Hard
B ?
N is 100X+10Y+Z (But all are same value) --> 111X (Hence we can say that N is a multiple of 111) -->
using this we know that N is divisible by 3 as the sum adds up to a multiple of 3. so 53N will also be divisible by 3.
Now, it’s given to us that the product 53N is a 5-digit integer comprised of five of the following six digits: 1, 2, 4, 6, 7, 9
The sum of these 6 numbers come out to be 29. We’re asked to select 5 out of the 6.
So if we subtract "2" from "29" we get "27" which is a multiple of 3.
Hence, "2" shouldn’t be selected out of the given 6 numbers.
Hope it makes sense