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What is the value of the three-digit integer \(t\) if \(t\)

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by BTGmoderatorLU » Wed Jul 03, 2019 2:16 pm

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Source: Princeton Review

What is the value of the three-digit integer \(t\) if \(t\) is divisible by \(9\)?

1. The tens digit and the hundreds digit of \(t\) are both \(7\).
2. The units digit of \(t\) is less than both the tens digit and the hundreds digit.

The OA is A
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Source: — Data Sufficiency |

by Jay@ManhattanReview » Wed Jul 03, 2019 11:27 pm
BTGmoderatorLU wrote:Source: Princeton Review

What is the value of the three-digit integer \(t\) if \(t\) is divisible by \(9\)?

1. The tens digit and the hundreds digit of \(t\) are both \(7\).
2. The units digit of \(t\) is less than both the tens digit and the hundreds digit.

The OA is A
Let's take each statement one by one.

1. The tens digit and the hundreds digit of \(t\) are both \(7\).

=> t = 77x; where x = units digit

t/9 = 77x/9 gives x = 4, a unique value. Thus, t = 774. Sufficient.

2. The units digit of \(t\) is less than both the tens digit and the hundreds digit.

If t is a multiple of 20, 30, 40, ...90, the above condition is fulfilled, while we get different values of t such as 180, 270, 360, ... 810. Insufficient.

The correct answer: A

Hope this helps!

-Jay
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