Let x and y be 2 positive integers such that x/y=12.12, what is the va

Question

Let x and y be 2 positive integers such that x/y=12.12, what is the value of y?

(1) 1/y is a terminating decimal.
(2) y is a double digit odd number.

andreagonzalez2k · Answer

x/y=1212/100
If we reduce the fraction we have
x/y=303/25

(1) 1/y is a terminating decimal
y can be 100, 50, 25, 1000... so insufficent
(2) y is a double digit odd number
if we multiply numerator and denominator by 3
303/25 = 909/75
so we have two options, insufficient

(1) and (2)
1/75 is not a terminating decimal because 75=3*25, so the only valid option is 25, sufficient

IMO C

AnantpriyaSingh · Answer

Hey, any reason for multiplying once by 3? Is it because we need an odd number? Also why just multiplied one?

andreagonzalez2k · Answer

We have three equivalent fractions whose denominator has double digit: 303/25, 606/50 (multiplying numerator and denominator by 2) and 909/75 (multiplying numerator and denominator by 3). The "next one" (multiplying numerator and denominator by 4) has a denominator with 3 digits (1212/100). From them 303/25 and 909/75 have a denominator which is an odd number. So we have two options and (2) is insufficient.

Bunuel · Answer

Let x and y be 2 positive integers such that x/y=12.12, what is the value of y?

Given x/y = 12.12 = 303/25, this implies that y is a positive multiple of 25. Therefore, it can be 25, 50, 75, 100, and so on.

(1) 1/y is a terminating decimal.

This implies that y has only 2s and 5s in its prime factorization, so y = 25*2^n*5^m, where m and n are nonnegative integers. Hence, possible values for y include 25*2^2 = 100, 25*5 = 125, and so on. Not sufficient.

(2) y is a double digit odd number.

This implies that y can be either 25 or 75. Not sufficient.

(1)+(2) y cannot be 75 since in that case 1/y = 1/75 would not result in a terminating decimal. Therefore, the only remaining value from (2) is 25. Sufficient.

Answer: C.

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Let x and y be 2 positive integers such that x/y=12.12, what is the va

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Let x and y be 2 positive integers such that x/y=12.12, what is the va

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