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The digits of a three-digit number add up to 18. If the ten’s digit is

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Joined: 02 Nov 2016
Posts: 4443
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The digits of a three-digit number add up to 18. If the ten’s digit is  [#permalink]

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New post 19 Nov 2018, 12:28
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

86% (01:31) correct 14% (01:50) wrong based on 93 sessions

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The digits of a three-digit number add up to 18. If the ten’s digit is twice the hundred’s digit and the hundred’s digit is 1/3 the unit’s digit, what is the number?

(A) 246
(B) 369
(C) 531
(D) 855
(E) 893

Source: Nova GMAT

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Re: The digits of a three-digit number add up to 18. If the ten’s digit is  [#permalink]

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New post 19 Nov 2018, 15:12
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Top Contributor
SajjadAhmad wrote:
The digits of a three-digit number add up to 18. If the ten’s digit is twice the hundred’s digit and the hundred’s digit is 1/3 the unit’s digit, what is the number?

(A) 246
(B) 369
(C) 531
(D) 855
(E) 893


The ten’s digit is twice the hundred’s digit
Check the answer choices . . .
For answer choices C, D and E, the ten’s digit is NOT twice the hundred’s digit
ELIMINATE C, D and E

We're left with:
(A) 246
(B) 369

The digits of a three-digit number add up to 18.
Check the remaining answer choices . . .
(A) 246. Sum of digits = 2 + 4 + 6 = 12
ELIMINATE A

By the process of elimination, the correct answer is B

Cheers,
Brent
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Re: The digits of a three-digit number add up to 18. If the ten’s digit is  [#permalink]

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New post 19 Nov 2018, 17:43
SajjadAhmad wrote:
The digits of a three-digit number add up to 18. If the ten’s digit is twice the hundred’s digit and the hundred’s digit is 1/3 the unit’s digit, what is the number?

(A) 246
(B) 369
(C) 531
(D) 855
(E) 893

Source: Nova GMAT


LET THE THREE DIGIT NO BE 100X+10Y+Z

GIVEN THAT X+Y+Z= 18
Y=2X, X=Z/3
X+2X+3X= 18
THEREFORE X=3
Y=6 AND Z=9

THEN NO IS 100*3+(10*6)+(1*9)=369

+1 FOR OPTION B
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Re: The digits of a three-digit number add up to 18. If the ten’s digit is  [#permalink]

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New post 19 Nov 2018, 22:21
1
Let a = Hundreds Digit Number, b = Tens Digit Number, c = Units Digit Number
a+b+c = 18 .... (i)
b = 2a & a = c/3 => 3a = c
(i)=> a + 2a + 3a = 18 => 6a = 18 => a = 3
so b = 6, c = 9
Number = 369 ...... ANSWER = B
GMAT Club Bot
Re: The digits of a three-digit number add up to 18. If the ten’s digit is   [#permalink] 19 Nov 2018, 22:21
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