The GMAT Sample Math question given below is from the topic Arithmetic Progressions. Problems on Arithmetic Progressions are quite easy if one understands that the basic concept behind AP is just an extrapolation of simple multiplication tables.
What is the sum of all 3 digit numbers that leave a remainder of '2' when divided by 3?
- 897
- 164,850
- 164,749
- 149,700
- 156,720
The correct choice is (B) and the correct answer is
164,850.
The smallest 3 digit number that will leave a remainder of 2 when divided by 3 is 101.
The next number that will leave a remainder of 2 when divided by 3 is 104, 107, ....
The largest 3 digit number that will leave a remainder of 2 when divided by 3 is 998.
So, the given series is an AP with the first term being 101 and the last term being 998 and thhe common difference being 3.
Sum of an AP =
We know that in an A.P., the nth term a
n = a
1 + (n - 1)*d
In this case, therefore, 998 = 101 + (n - 1)* 3
i.e., 897 = (n - 1) * 3
Therefore, n - 1 = 299
Or n = 300.
Sum of the AP will therefore, be
= 164,850
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