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What is the three-digit number abc, given that a, b, and c

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What is the three-digit number abc, given that a, b, and c [#permalink] New post 31 Jan 2012, 17:59
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Question Stats:

58% (02:48) correct 42% (01:56) wrong based on 180 sessions
What is the three-digit number abc, given that a, b, and c are the positive single digits that make up the number?

(1) a = 1.5b and b = 1.5c
(2) a = 1.5x + b and b = x + c, where x represents a positive single digit

[Reveal] Spoiler:
As the OA is not given, for me the answer will be E and this is how I got it. Please let me know if I am right or wrong.

Statement 1 --> Insufficient because b and c can take any single value.

Statement 2 --> Insufficient as again b and c can take any values.

Combining the two statements

a = 1.5x + b and b = x + c ------------------------------------(From Statement 2)
a = 1.5b and b = 1.5c ----------------------------------------(From Statement 1)

Substituting 1 in 2

we get b = 3x and x = 0.5 c. again b and c can take any value and therefore my answer is E.
[Reveal] Spoiler: OA

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MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610 :-(


Last edited by Bunuel on 23 May 2013, 03:47, edited 2 times in total.
Added the OA
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Re: +ve single digits [#permalink] New post 31 Jan 2012, 18:23
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What is the three-digit number abc, given that a, b, and c are the positive single digits that make up the number?

(1) a = 1.5b and b = 1.5c --> a/b=3/2=9/6 and b/c=3/2=6/4 --> a/b/c=9/6/4 and as a, b, and c are the positive single digits, then a=9, b=6 and c=4 --> abc=964. Sufficient.

(2) a = 1.5x + b and b = x + c, where x represents a positive single digit --> multiple values are possible, for example: if x=2 then a=3+b and b=2+c --> abc can 631 (for c=1) be or 742 (for c=2). Not sufficient.

Answer: A.
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Re: What is the three-digit number abc, given that a, b, and c [#permalink] New post 30 Sep 2013, 10:58
enigma123 wrote:
What is the three-digit number abc, given that a, b, and c are the positive single digits that make up the number?

(1) a = 1.5b and b = 1.5c
(2) a = 1.5x + b and b = x + c, where x represents a positive single digit



1) a=1.5b ...........................1
b=1.5c ...........................2

the number is 100a +10b +c = n

c=c
b=1.5c , put value of b in given equation no.1
a=2.25c

n = 225c+25c+c = 241c .. we know c is an integer and in this case it can take four values from 1 to 4 .. for values greater than 4, "n" will become 5 digit number.
now a=2.25c .. we know a is also an integer .. from the possible values of c we have i.e. 1,2,3,4 .. only 4 will make a an integer ..

hence,
a = 2.25*4=9
b = 1.5*4=6
c = 4

n = 964


2) well, this one is easy just put values in 100a+10b+c .. you'll get 260x+110c .. too many possibilities
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Re: What is the three-digit number abc, given that a, b, and c [#permalink] New post 16 Oct 2013, 05:26
(1) a = 1.5b b = 1.5c
a = 2.25c

a must equal an integer and the only way this is satisfied is if c = 4 (2.25 * 4 = 9)

b = 1.5c = 1.5(4) = 6
a = 1.5b = 1.5(6) = 9

all checks out and no other possibilities so (1) is sufficient.

(2) Too many possibilities.
a = 1.5x + b and b = x + c
a = 1.5x + x + c = 2.5x + c
a = 2.5x + c --> many possible values for 'a' and 'c'. Not sufficient.


Answer: A
Re: What is the three-digit number abc, given that a, b, and c   [#permalink] 16 Oct 2013, 05:26
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