If x^2 < x and x is written as a terminating decimal, does x have a nonzero hundredths digit?
(1) 10x is not an integer.
(2) 100x is an integer.
OAC
Please explain.
Many thanks in advance.
Kavin
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does x have a nonzero hundredths digit?
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Hi Kavin,
This DS question can be solved with a mix of Number Property rules and TESTing VALUES.
We're told that X^2 < X and that X is written as a terminating decimal. The only values that fit this restriction are positive fractions, so 0 < X < 1. We're asked if X has a non-zero hundredths digit. This is a YES/NO question.
(1) 10X is not an integer.
IF...
X = .11
10X = 1.1
and the answer to the question is YES.
IF...
X = .101
10X = 1.01
and the answer to the question is NO.
Fact 1 is INSUFFICIENT
(2) 100X is an integer.
IF...
X = .11
100X = 11
and the answer to the question is YES.
IF...
X = .10
100X = 10
and the answer to the question is NO.
Fact 2 is INSUFFICIENT
Combined, we know...
10X is not an integer.
100X is an integer.
Multiplying a number by 100 'shifts' the decimal point two places to the 'right'; since 100X is an INTEGER, that means that X CANNOT have a non-zero number past the hundredths digit (re: X=1.23 is possible, since 123 is an integer, but X=1.234 is NOT possible, since 123.4 is NOT an integer). This means that X can have no more than 2 digits to the right of the decimal point (and anything past the hundredths digit MUST be a zero).
Combined with the above deduction, since 10X is NOT an integer, we also know that the hundredths digit CANNOT be 0 (otherwise we would end up with 10X as an integer). The answer to the question is ALWAYS YES.
Combined, SUFFICIENT
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
This DS question can be solved with a mix of Number Property rules and TESTing VALUES.
We're told that X^2 < X and that X is written as a terminating decimal. The only values that fit this restriction are positive fractions, so 0 < X < 1. We're asked if X has a non-zero hundredths digit. This is a YES/NO question.
(1) 10X is not an integer.
IF...
X = .11
10X = 1.1
and the answer to the question is YES.
IF...
X = .101
10X = 1.01
and the answer to the question is NO.
Fact 1 is INSUFFICIENT
(2) 100X is an integer.
IF...
X = .11
100X = 11
and the answer to the question is YES.
IF...
X = .10
100X = 10
and the answer to the question is NO.
Fact 2 is INSUFFICIENT
Combined, we know...
10X is not an integer.
100X is an integer.
Multiplying a number by 100 'shifts' the decimal point two places to the 'right'; since 100X is an INTEGER, that means that X CANNOT have a non-zero number past the hundredths digit (re: X=1.23 is possible, since 123 is an integer, but X=1.234 is NOT possible, since 123.4 is NOT an integer). This means that X can have no more than 2 digits to the right of the decimal point (and anything past the hundredths digit MUST be a zero).
Combined with the above deduction, since 10X is NOT an integer, we also know that the hundredths digit CANNOT be 0 (otherwise we would end up with 10X as an integer). The answer to the question is ALWAYS YES.
Combined, SUFFICIENT
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
