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06 Aug 2021, 04:45
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
85% (01:43) correct
15%
(02:15)
wrong
based on 105
sessions
History
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The highest common factor and the least common multiple of two positive integers are 7 and 140, respectively. If the numbers are between 20 and 45, what is the sum of the numbers ?
(A) 77
(B) 70
(C) 63
(D) 56
(E) 47
(A) 77
(B) 70
(C) 63
(D) 56
(E) 47
06 Aug 2021, 05:01
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Bunuel
Product of two numbers is equal to the product of their LCM and HCF.
Let the numbers be a and b, where a=7x and b=7y.
So a*b=7x*7y=7*140=2*2*5*7*7
Now a and b are greater than 20, so 7x>20….x>2
Similarly y>2
So, x*y=2*2*5=4*5……x+y=5+4=9
Sum =7*(x+y)=7*9=63
C
06 Aug 2021, 05:23
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HCF = 7
LCM = 140 = 2*2*5*7
Let's say the numbers are x & y
Since the HCF is 7, the numbers are multiple of 7.
Possible numbers between 20 & 45 =>
21 = 3*7
28= 2*2*7
35 = 5*7
42 = 2*3*7
Since the LCM's prime factorization doesn't have any 3......we can reject 21 and 42
So, the two numbers are 28 & 35
Sum = 28 + 35 = 63
OA should be C
LCM = 140 = 2*2*5*7
Let's say the numbers are x & y
Since the HCF is 7, the numbers are multiple of 7.
Possible numbers between 20 & 45 =>
21 = 3*7
28= 2*2*7
35 = 5*7
42 = 2*3*7
Since the LCM's prime factorization doesn't have any 3......we can reject 21 and 42
So, the two numbers are 28 & 35
Sum = 28 + 35 = 63
OA should be C
