VJesus12 wrote: ↑

Wed Jun 24, 2020 5:38 am

The digit 7 appears in how many of the first thousand positive integers?

A. 143
B. 152
C. 171
D. 190
E. 271

[spoiler]OA=E[/spoiler]

Source: GMAT Prep

Let's calculate how many integers from 1-99 are there in which '7' appears at least once.

The integers in which '7' appears in units' place: 7, 17, 27, ..., 97: So there 10 numbers;
The integers in which '7' appears in tens' place: 70, 71, ... 79: So there 10 numbers

But, note that '77' is counted double.

So, from 1-99 are there are 10 + 10 – 1 = 19 integers in which '7' appears.

Same goes for 100-199; 200-299; 300-399, ..., and 900-999.

Total such integers = 19*10 = 190;

But this is an incomplete count. From 701-799, there are 100 – 19 = 81 integers that were not counted.

So, the required integers = 190 + 81 = 271.

Correct answer: E

Hope this helps!

-Jay
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VJesus12 wrote: ↑

Wed Jun 24, 2020 5:38 am

The digit 7 appears in how many of the first thousand positive integers?

A. 143
B. 152
C. 171
D. 190
E. 271

[spoiler]OA=E[/spoiler]

Source: GMAT Prep

Solution:

In each of the hundreds (i.e., 1-99, 100s, 200s, etc.) of the first 1000 positive integers, except for the 700s, the digit 7 appears in 19 integers, either as the units digit or the tens digit or both. In the 700s, 7 appears in every integer; therefore, the total number of integers that has (at least) one digit of 7 is:

9 x 19 + 100 = 171 + 100 = 271

Answer: E