When integer a is divided by 4 . . .

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members; Thanked: 6 times

by Vincen » Tue Dec 12, 2017 10:44 am

When integer a is divided by 4 the remainder is 2, and when integer b is divided by 5 the remainder is 1. How many integers between 20 and 29, inclusive, CANNOT be the sum a + b?

A. Zero
B. One
C. Two
D. Three
E. Four

The OA is A.

I don't know how to solve this PS question. I don't where I should start. Experts, may you give me some help here? I would be thankful.

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Source: Beat The GMAT — Problem Solving | Tue Dec 12, 2017 10:44 am

EconomistGMATTutor: GMAT Instructor; Posts: 555; Joined: Wed Oct 04, 2017 4:18 pmFollowed by: 12 members; Thanked: 180 times

Answer

by EconomistGMATTutor » Tue Dec 12, 2017 11:58 am

Hello.

Let's take a careful look at your question.

When "a" is divided by 4 the remainder is "2". Possible values for "a":
2, 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, . . . .

When "b" is divided by 5 the remainder is "1". Possible values for "b":
1, 6, 11, 16, 21, 26, 31, 36, 41, . . .

The integers between 20 and 29 can be written as follows:

20 = 14 + 6
21 = 10 + 11
22 = 6 + 16
23 = 2 + 21
24 = 18 + 6
25 = 14 + 11
26 = 10 + 16
27 = 26 + 1
28 = 22 + 6
29= 18 + 11

So, ALL the integers can be the sum a+b.

This is why the correct answer is A.

I hope this explanation may help you.

Feel free to ask me if you have a doubt.

Regards.

GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Tue Jan 02, 2018 9:22 am

Vincen wrote:When integer a is divided by 4 the remainder is 2, and when integer b is divided by 5 the remainder is 1. How many integers between 20 and 29, inclusive, CANNOT be the sum a + b?

A. Zero
B. One
C. Two
D. Three
E. Four

We use the "quotient remainder theorem," which states: dividend = divisor x quotient + remainder.
We can create the following equations:

a = 4Q + 2

b = 5Z + 1

So, a can be 2, 6, 10, 14, 18, 22, and 26.

So, b can be 1, 6, 11, 16, 21, and 26.

We see that a + b can be the following:

14 + 6 = 20

10 + 11 = 21

6 + 16 = 22

22 + 1 = 23

18 + 6 = 24

14 + 11 = 25

10 + 16 = 26

6 + 21 = 27

22 + 6 = 28

18 + 11 = 29

Answer: A

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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