If A 3-Digit Positive Integer Is A Multiple Of 7 GMAT Problem Solving

Number of multiples of 7: 999/7 – 100/7 = 142 – 14 = 128

Number of multiples of 35: 999/35 – 100/35 = 28 – 2 = 26

Probability that a multiple of 7 will be a multiple of 5 = 26/128=13/64

Correct option: D

3-digit positive integer is a multiple of 7: 105, 112, 119,..., 994.

Calculating 994 = 105 + (n-1)x7, we know that 994 is the 128^th (=n) element of the series.

3-digit positive integer that is a multiple of 5 and 7: 105, 140, 175,..., 980.

Calculating 980 = 105 + (n-1)x35, we know that 980 is the 26^th (=n) element of the series.

Thus, the probability that it will be both multiple of 5 and 7 is 26/128=13/64

Correct option: D

So 100 < 7k < 999 (k is an integer)

14 < k < 142

k = 142 - 14 = 128

To find whether these numbers are a multiple of 5, we need to check for LCM (5,7) = 35 multiplicity.

Also, 100 < 35k' < 999 (k' is an integer)

2 < k' < 28

k' = 28 - 2 = 26

Probability = 26/128=13/64 

Correct option: D