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17 Oct 2018, 01:21
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B
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:
82% (01:37) correct
18%
(01:54)
wrong
based on 312
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If x is the greatest common divisor of 90 and 18, and y is the least common multiple of 51 and 34, then x + y =
A. 111
B. 120
C. 213
D. 222
E. 231
A. 111
B. 120
C. 213
D. 222
E. 231
17 Oct 2018, 01:51
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Finding x - GCD (90 ,18)
90 = 2 x \(3^2\) x 5
18 = 2 x \(3^2\)
--> x = 2 x \(3^2\) = 18
Finding y - LCM (51,34)
51 = 3 x 17
34 = 2 x 17
--> y = 2 x 3 x 17 = 102
--> x + y = 102 + 18 = 120
--> Option B is the answer
Let me know your thought. Thank you
90 = 2 x \(3^2\) x 5
18 = 2 x \(3^2\)
--> x = 2 x \(3^2\) = 18
Finding y - LCM (51,34)
51 = 3 x 17
34 = 2 x 17
--> y = 2 x 3 x 17 = 102
--> x + y = 102 + 18 = 120
--> Option B is the answer
Let me know your thought. Thank you
17 Oct 2018, 01:52
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Bunuel
To find the GCD and LCM of two numbers always denote the numbers in the prime factorization form -
First pair:
\(18 = 2^1*3^2\)
\(90 = 2^1*3^2*5^1\)
To find GCD of these two numbers - find the common factors ( along with powers) : So GCD would be : \(2^1*3^2 = 18\)
Second pair:
\(51 = 3^1*17^1\)
\(34 = 2^1*17^1\)
So GCD is \(17^1 = 17\) and the LCM is (First number * Second number)/GCD = \(\frac{(3^1*17^1*2^1*17^1)}{17^1} =\)\(3*2*17\)
Hence the question is asking \(18 + 6*17 = 18 + 102 = 120\)
Hence Option (B) is our choice.
Regards,
Gladi
