Multiple of 14, 7

A and B are two multiples of 14, and Q is the set of consecutive integers between A and B, inclusive. If Q contains 9 multiples of 14, how many multiples of 7 are there in Q?

20
19
18
17
16

Between every two consecutive multiples of 14, there will be one multiple of 7

example: 14,15,16,17,....,21,22,23,..28

Between two multiples of 14 (14 and 28) lies one multiple of 7 ( 21)

So if there are 9 multiples of 14 in Q, the number of mltiples of 7 would be = 9 + 8 = 17

Option D

OA is 17

@rijul
if we consider A=14 and B =154
We will have 9 multiples of 14 between them i.e. 28 42 56 70 84 98 112 126 140 = 9
And between each of them there will be 8 multiple of 8 so total = 8

But, if is set Q is containing consecutive numbers between 14 to 154, there will be also 21( between 14 and 28) and 147 ( between 140 and 154) so total count equals 2

So shouldn't answer be 19? Plz clarify

kakz wrote:@rijul
if we consider A=14 and B =154
We will have 9 multiples of 14 between them i.e. 28 42 56 70 84 98 112 126 140 = 9
And between each of them there will be 8 multiple of 8 so total = 8

But, if is set Q is containing consecutive numbers between 14 to 154, there will be also 21( between 14 and 28) and 147 ( between 140 and 154) so total count equals 2

So shouldn't answer be 19? Plz clarify

A and B are two multiples of 14, and Q is the set of consecutive integers between A and B, INCLUSIVE. If Q contains 9 multiples of 14, how many multiples of 7 are there in Q?

Hey kakz,
Have a look at the highlighted part.
Do you see where you are going wrong?
Notify me if you still have a doubt

karthikpandian19 wrote:A and B are two multiples of 14, and Q is the set of consecutive integers between A and B, inclusive. If Q contains 9 multiples of 14, how many multiples of 7 are there in Q?

20
19
18
17
16

Since Q is the set of consecutive integers between A and B, inclusive, we can let A = 1 x 14 = 14 and B = 9 x 14 = 126. Thus, the number of multiples of 7 in Q is:

(126 - 14)/7 + 1 = 112/7 + 1 = 17

Answer: D