If r and t are three-digit positive integers,

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jjjinapinch: Senior | Next Rank: 100 Posts; Posts: 83; Joined: Mon Jul 24, 2017 8:16 am; Followed by:1 members

If r and t are three-digit positive integers,

by jjjinapinch » Wed Aug 02, 2017 11:13 am

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If r and t are three-digit positive integers, is r greater than t ?
(1) The tens digit of r is greater than each of the three digits of t.
(2) The tens digit of r is less than either of the other two digits of r.

Official Guide question
Answer: C

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Source: Beat The GMAT — Data Sufficiency | Wed Aug 02, 2017 11:13 am

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by [email protected] » Wed Aug 02, 2017 7:08 pm

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Hi jjjinapinch,

We're told that R and T are both three-digit positive integers. We're asked if R is greater than T. This is a YES/NO question. We can solve it by TESTing VALUES.

1) The TENS digit of R is greater than each of the three digits of T.

IF....
R = 191 and T = 111, then the answer to the question is YES.
R = 191 and T = 888, then the answer to the question is NO.
Fact 1 is INSUFFICIENT

2) The TENS digit of R is less than either of the other two digits of R.

Fact 2 tells us NOTHING about the value of T, so there's no way to determine whether R is greater than T or not.
Fact 2 is INSUFFICIENT

Combined, we know:
-The TENS digit of R is greater than each of the three digits of T.
-The TENS digit of R is less than either of the other two digits of R.

With Fact 1, we know that the TENS digit of R is greater than all 3 digits in T, but we had no way to compare the HUNDREDS digits of R and T (so we didn't know which number was bigger). With the information in Fact 2 though, we know that the TENS digit of R is LESS than the HUNDREDS digit of R. Thus, we can create the following inequality:

(Hundreds digit of R) > (Tens digit of R) > (ANY digit in T)

eg. R = 870 and T = 512

Since the HUNDREDS digit of R is greater than EACH digit in T (including the HUNDREDS digit of T), R will ALWAYS be greater than T.
Combined, SUFFICIENT

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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by Scott@TargetTestPrep » Fri Nov 17, 2017 12:01 pm

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jjjinapinch wrote:If r and t are three-digit positive integers, is r greater than t ?
(1) The tens digit of r is greater than each of the three digits of t.
(2) The tens digit of r is less than either of the other two digits of r.

We are given that r and t are three-digit positive integers and need to determine whether r is greater than t.

Statement One Alone:

The tens digit of r is greater than each of the three digits of t.

Statement one alone is not sufficient to answer the question. For example, if r = 190 and t = 180, then r is greater than t; however, if r = 190 and t = 210, then r is less than t.

Statement Two Alone:

The tens digit of r is less than either of the other two digits of r.

Since we know nothing about t, statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Using statements one and two, we see that the tens digit of r is greater than each of the three digits of t and that the tens digit of r is less than either of the other two digits of r.

Thus, we can say that all digits of r must be greater than all digits of t, so we can say that r is greater than t.

Answer: C

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