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The digital sum of a number is the sum of its digits.

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The digital sum of a number is the sum of its digits.

by Vincen » Thu Nov 02, 2017 8:36 am
The digital sum of a number is the sum of its digits. For how many of the positive integers 24-125 inclusive is the digital sum a multiple of 7?

A 7
B 8
C 14
D 16
E 20

The OA is C.

Do I have to make the entire list? Is there another way to solve this PS question? Experts, I want to see you explanation for this exercise. Thanks.
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by Brent@GMATPrepNow » Thu Nov 02, 2017 9:16 am
Vincen wrote:The digital sum of a number is the sum of its digits. For how many of the positive integers 24-125 inclusive is the digital sum a multiple of 7?

A 7
B 8
C 14
D 16
E 20
Listing and counting is a fast approach.
25
34
43
52
61
70
106
115

Answer: B

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by [email protected] » Fri Nov 03, 2017 1:55 pm
Hi Vincen,

Based on the answer choices, you know that there are at least 7 numbers that fit the given description, but no more than 20. Thus, listing them all out shouldn't be too difficult. You might also find it useful to organize your numbers by 'group'

We're restricted to the numbers 24 to 125, inclusive. We're asked to find the numbers whose digits add up to a MULTIPLE of 7:

Numbers with digits that add up to 7:
25 and 52
34 and 43
61
70
106
115
124

Numbers with digits that add up to 14:
59 and 95
68 and 86
77

Total numbers = 9+5 = 14

Final Answer: C

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Rich
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by Scott@TargetTestPrep » Thu Oct 31, 2019 5:17 pm
Vincen wrote:The digital sum of a number is the sum of its digits. For how many of the positive integers 24-125 inclusive is the digital sum a multiple of 7?

A 7
B 8
C 14
D 16
E 20

The OA is C.

Do I have to make the entire list? Is there another way to solve this PS question? Experts, I want to see you explanation for this exercise. Thanks.
First, let's determine the two-digit numbers in the range of 24 to 99, inclusive, that have a digital sum of a multiple of 7:

To get a digital sum of 7, it needs to be 70, 61, 25, 52, 34 or 43.

To get a digital sum of 14, it needs to be 77, 68, 86, 59, or 95.

Since no digital sum of a two-digit number can be 21 or more, we see that there are 11 2-digit numbers that meet the criteria.

Now, let's determine the three-digit numbers in the range of 100 to 125, inclusive, that have a digital sum of a multiple of 7:

To get a digital sum of 7, it needs to be 106, 115 or 124.

Since no digital sum of a three-digit number (no more than 125) can be 14 or more, we see that we have a total of three 3-digit numbers that fit the criteria..

Therefore, there are a total of 11 + 3 = 14 such numbers.

Answer: C

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