How many numbers between 1 and 200, inclusive, have a 2 in

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Max@Math Revolution: Elite Legendary Member; Posts: 3991; Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members; Location: Las Vegas, USA; Thanked: 19 times

by Max@Math Revolution » Mon Feb 11, 2019 11:40 pm

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[GMAT math practice question]

How many numbers between 1 and 200, inclusive, have a 2 in the units place and are divisible by 4?

A. 8
B. 9
C. 10
D. 11
E. 12

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by GMATGuruNY » Tue Feb 12, 2019 3:26 am

Max@Math Revolution wrote:[GMAT math practice question]

How many numbers between 1 and 200, inclusive, have a 2 in the units place and are divisible by 4?

A. 8
B. 9
C. 10
D. 11
E. 12

An integer is divisible by 4 if its last two digits form a multiple of 4.
Two-digit multiples of 4 with a units digit of 2:
12, 32, 52, 72, 92
Since the last two digits must be one of the options above, between 1 and 200 there are 10 integers that have a units digit of 2 and are divisible by 4:
12, 32, 52, 72, 92
112, 132, 152, 172, 192

The correct answer is C.

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by Scott@TargetTestPrep » Wed Feb 13, 2019 6:33 pm

Max@Math Revolution wrote:[GMAT math practice question]

How many numbers between 1 and 200, inclusive, have a 2 in the units place and are divisible by 4?

A. 8
B. 9
C. 10
D. 11
E. 12

The numbers are 12, 32, 52, etc. We see that the first number is 12 and the last number will be 192 and the numbers form an arithmetic progression with a common difference of 20. Therefore, there are (192 - 12)/20 + 1 = 180/20 + 1 = 9 + 1 = 10 such numbers.

Answer: C

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Max@Math Revolution: Elite Legendary Member; Posts: 3991; Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members; Location: Las Vegas, USA; Thanked: 19 times

by Max@Math Revolution » Thu Feb 14, 2019 12:44 am

=>

In order for a number with 2 in the units place to be divisible by 4, the last two digits must be one of 12, 32, 52, 72 and 92.
Thus, the numbers between 1 and 200, inclusive, satisfying this property are
12, 32, 52, 72, 92, 112, 132, 152 and 172.

There are 8 such numbers. Therefore, A is the answer.
Answer: A

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