How many integers between 100 to 300, inclusive,

Question

Q58. How many integers between 100 to 300, inclusive, are multiples of both 4 and 6 but not multiples of 5?​

A. 3 ​

B. 4​

C. 13​

D. 16​

E. 17​

garcmillan · Accepted Answer

Hi all,

For this kind of questions we need to follow the next steps:

1) find the LCM between 4 and 6 ->  LCM is 12

2) find the first multiple of 12 after 100 -> Sum of digits need to be a multiple of 3 -> 102 (it is not multiple of 4), 105 (it is not a multiple of 2),  108  (it is a multiple of 4 and 3, and therefore of 12)

3) find the first multiple of 12 before 300 -> Sum of digits need to be a multiple of 3 -> 297 (it is not a multiple of 2), 294 (it is not a multiple of 4), 291 (it is not a multiple of 2),  288  (it is a multiple of 4 and 3, and therefore of 12)

4) find the numbers between 288 and 108 with increases of 12 (both inclusive) -> (288-108)/12 + 1 (the +1 is because both are inclusive) =  16

5) then we know that we need to deduct the multiples of 60 (multiple of 12 and 5). Multiples of 60 are 60, 120, 180, 240, 300 (only 120, 180 and 240 fall within the range),

Answer is 16-3 =  13

ANSWER C

Advice: these steps can be used in any questions of this kind, you just need to use different numbers. This way you can solve the questions very quickly

Davinder1209 · Answer

13

It should be multiple of 12 but should notbe multiple of 60.
Hence 108 to 300 is 17 
120 , 180 , 240 , 300 =4
Toral 17-4 =13

Posted from my mobile device

CrackverbalGMAT · Answer

By the counting principle, the number of multiples between 2 numbers is given by the below equation

\(\frac{Largest - Smallest }{Divisor}\) + 1, where The divisor is the number whose multiples we need.

Multiples of 4 and 6 but not 5. Multiples of LCM (4,6) = 12 - Multiples of LCM(4,6,5) = 60

For Multiples of 12.

The smallest number > 100 divisible by 12 = 108

The largest number < 300 divisible by 12 = 300

Number of multiples of 12 = \frac{300 - 108}{12} + 1 = \frac{192}{12} + 1 = 16 + 1 = 17

For Multiples of 60.

The smallest number > 100 divisible by 60 = 120

The largest number < 300 divisible by 60 = 300

Number of multiples of 60 = \frac{300 - 120}{60} + 1 = \frac{180}{60} + 1 = 3 + 1 = 4

The required number of multiples = 17 - 4 = 13

Option C

Arun Kumar

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How many integers between 100 to 300, inclusive,

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How many integers between 100 to 300, inclusive,

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