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What is the value of the three-digit integer t if t is divisible by 9

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What is the value of the three-digit integer t if t is divisible by 9  [#permalink]

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New post 20 Mar 2017, 12:18
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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.

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Re: What is the value of the three-digit integer t if t is divisible by 9  [#permalink]

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New post 20 Mar 2017, 13:18
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What is the value of the three-digit integer t if t is divisible by 9 ?

For a number to be divisible by 9, the sum of its digit must be divisible by 9.

Statement (1) The tens digit and the hundreds digit of t are both 7.
As both the hundreds and tens digit are 7, the sum of the digits comes to 14. Plus adding the unit's digit (let us assume unit's digit as x), therefore 14+x should be divisible by 9, for T to be divisible by 9.

18 is the closest multiple of 9 to 14. Hence x is 4.
Next multiple of 9 is 27. Which makes x = 13, which cannot be the unit's digit. Hence T is 774.
Statement 1 is sufficient.


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

As units digit of t is less than both the tens digit and the hundreds digit, we can multiple combinations such as 531, 621, 954..

As with the given condition, there can be multiple values of T, this statement is not sufficient.

Answer is A
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Re: What is the value of the three-digit integer t if t is divisible by 9  [#permalink]

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New post 24 Nov 2019, 12:52
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SajjadAhmad wrote:
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.


----ASIDE------
Key Property: If an integer is divisible by 9, then the sum of its digits will be divisible by 9
For example, 576 is divisible by 9. Notice that 5 + 7 + 6 = 18, and 18 is divisible by 9
----------------

Given: t is a 3-digit integer that is divisible by 9
From the above property we can conclude that the SUM of t's three digits must be divisible by 9

Target question: What is the value of t?

Statement 1: The tens digit and the hundreds digit of t are both 7.
So, t = 77k , where k = the unknown units digit
Since the SUM of t's three digits must be divisible by 9, we know that 7 + 7 + k must equal some value that is divisible by 9.
Since k is a single-digit, it MUST be the case that k equals 4. (when k = 4, we see that t = 774, which is divisible by 9)
The answer to the target question is t = 774
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The units digit of t is less than both the tens digit and the hundreds digit.
There are several 3-digit integers that satisfy statement 2 (and the given condition that t is divisible by 9). Here are two:
Case a: t = 621. In this case, the answer to the target question is t = 621
Case b: t = 630. In this case, the answer to the target question is t = 630
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

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Brent
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Re: What is the value of the three-digit integer t if t is divisible by 9   [#permalink] 24 Nov 2019, 12:52
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