x is a two-digit positive integer. y is obtained by multiplying the te

Question

x is a two-digit positive integer. y is obtained by multiplying the tens place of x by 2. Is y >  \frac{x}{6}  ?

Statement 1: 20 < x < 30
Statement 2: y = 10

stne · Answer

1: 20 < x < 30 if x=21 , y = 4 Is 4 > \frac{21}{6}= 3\frac{1}{2}, Yes. If x= 29, y=4 Is 4 > \frac{29}{6} = 4 \frac{5}{6}, No. INSUFF. 2: y = 10 Then 50 \leq x \leq 59 If x= 50 Is 10 > \frac{50}{6} = 8\frac{2}{6}, Yes If x=59 Is 10 > \frac{59}{6} = 9\frac{5}{6}, Yes SUFF. Ans B

YB10 · Answer

Don’t both statements need to be consistent with each other? How can x be in 20s when y is 10.

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gmatophobia · Answer

Assume x = mn m ⇒ tens place of x n ⇒ units place of x x = 10m + n Contraints 0 \leq m \leq 9 0 \leq n \leq 9 y = 2m Question 2m > \frac{10m + n}{6} 12m > 10m + n 2m > n Statement 1 20 < x < 30 m = 2 2m = 4 If n = 1 → Is 2m > n ? ⇒ Yes If n = 9 → Is 2m > n ? ⇒ No As we are getting contradicting answer, Statement 1 is not sufficient. Statement 2 y = 10 2m = 10 From the constraints above, we know that the maximum value of n = 9 Hence, we can conclude that 2m is always greater than n Statement 2 alone is sufficient to answer the question. Option B

x is a two-digit positive integer. y is obtained by multiplying the te

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