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G.C.F and L.C.M

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G.C.F and L.C.M

by B166418 » Wed Nov 07, 2012 7:59 pm
X and Y are possitive integers,what is value of XY

(1) Greatest common factor of X and Y is 10
(2) Least common multiple of X and y is 180


A Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient.
D EACH statement ALONE is sufficient.
E Statements (1) and (2) TOGETHER are NOT sufficient.
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Source: — Data Sufficiency |

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by Anurag@Gurome » Wed Nov 07, 2012 8:02 pm
B166418 wrote:X and Y are possitive integers,what is value of XY

(1) Greatest common factor of X and Y is 10
(2) Least common multiple of X and y is 180


A Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient.
D EACH statement ALONE is sufficient.
E Statements (1) and (2) TOGETHER are NOT sufficient.
Product of two positive integers = (LCM of the integers)*(GCF of the integers)
Hence, we need both the statements to answer the question.

The correct answer is C.
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by Anurag@Gurome » Wed Nov 07, 2012 8:03 pm
B166418 wrote:X and Y are possitive integers,what is value of XY

(1) Greatest common factor of X and Y is 10
(2) Least common multiple of X and y is 180


A Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient.
D EACH statement ALONE is sufficient.
E Statements (1) and (2) TOGETHER are NOT sufficient.
Picking Numbers Approach:

Statement 1: Consider the following two cases,
x = 10 and y = 20 ---> xy = 200
x = 10 and y = 30 ---> xy = 300

Not sufficient

Statement 2: Consider the following two cases,
x = 4 and y = 45 ---> xy = 180
x = 90 and y = 180 ---> xy = 90*1800

Not sufficient

1 & 2 Together: xy = 10*180 = 1800
Sufficient

The correct answer is C.
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Gurome, Inc.
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