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09 Apr 2021, 14:00
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52% (02:16) correct
48%
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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?
A. 20
B. 19
C. 18
D. 17
E. 16
A. 20
B. 19
C. 18
D. 17
E. 16
09 Apr 2021, 14:41
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Let's say A = 1*14 = 14 and B = 9*14 = 126
Therefore, Q contains all integers from 14 to 126 (inclusive)
Number of multiples in a set of integers:
(biggest multiple - smallest multiple)/given number + 1
(126 - 14)/7 + 1
= 112/7 + 1
= 16 + 1
= 17
Answer D
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Therefore, Q contains all integers from 14 to 126 (inclusive)
Number of multiples in a set of integers:
(biggest multiple - smallest multiple)/given number + 1
(126 - 14)/7 + 1
= 112/7 + 1
= 16 + 1
= 17
Answer D
Posted from my mobile device
General Discussion
09 Apr 2021, 15:43
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From a theoretical point of view:
\(A = n*14 = n*7*2\)
\(B = (n+8)*14 = (n+8)*7*2\)
The number of multiples in a set of consecutive integers:
(biggest multiple - smallest multiple)/given number + 1
Since A and B have 7 as a factor, both numbers are a multiple of 7.
Therefore, the biggest multiple of 7 in this set of numbers is B and the smallest multiple is A
\(\frac{(n+8)*7*2 - n*7*2}{7} +1\) --> simplify
\(= \frac{7*2*(n+8-n)}{7} + 1\) --> simplify the parentheses
\(= \frac{7*2*8}{7} + 1\) --> cancel out the 7's
\(= 2*8 + 1\)
\(= 17\)
Posted from my mobile device
\(A = n*14 = n*7*2\)
\(B = (n+8)*14 = (n+8)*7*2\)
The number of multiples in a set of consecutive integers:
(biggest multiple - smallest multiple)/given number + 1
Since A and B have 7 as a factor, both numbers are a multiple of 7.
Therefore, the biggest multiple of 7 in this set of numbers is B and the smallest multiple is A
\(\frac{(n+8)*7*2 - n*7*2}{7} +1\) --> simplify
\(= \frac{7*2*(n+8-n)}{7} + 1\) --> simplify the parentheses
\(= \frac{7*2*8}{7} + 1\) --> cancel out the 7's
\(= 2*8 + 1\)
\(= 17\)
Posted from my mobile device
