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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When integer a is divided by 4 . . .
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EconomistGMATTutor
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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.
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.
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Jeff@TargetTestPrep
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We use the "quotient remainder theorem," which states: dividend = divisor x quotient + remainder.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 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
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