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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]

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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
(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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Last edited by Bunuel on 23 May 2013, 03:47, edited 2 times in total.
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Re: +ve single digits [#permalink]

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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]

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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]

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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
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Re: What is the three-digit number abc, given that a, b, and c [#permalink]

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Re: What is the three-digit number abc, given that a, b, and c [#permalink]

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New post 06 Oct 2015, 13:15
Bunuel 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 --> 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.

Here is another way to solve this question.
Question Stem: abc with a, b, c are the positive single digits -> abc = 100a + 10b + c
(1) a = 3b/2
b = 3c/2
=> abc = 241c and a = 9c/4 -> c must be 4 to make a a positive single digit.
=> abc = 241 x 4 = 964 -> Sufficient.
(2) a = 3x/2; b = x + c
=> abc = 260x + 111c. Many possible for x and c -> Not sufficient.

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

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New post 21 Sep 2016, 10:42
Another way to look at it is
1. a=3/2 b and b=3/2 c and all the digits are obviously positive integers.
=> both b and c are multiples of 2
=> c=2^n , where n is an integer and n>1
=> c=4 gives b=6 and a=9 , while c=8 gives b=12(invalid).
hence number is 964. SUFFICIENT

2. a=3/2x+b, b=x+c
All that we can infer is x is definitely even. There is no constraint on c. Multiple options possible
Hence INSUFFICIENT
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Re: What is the three-digit number abc, given that a, b, and c [#permalink]

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New post 01 Nov 2016, 05:51
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



I took some extra time to test additional values...to make sure B is not sufficient...

1. a=1.5b, b=1.5c
only option that works - c=4, b=6, a=8.
sufficient.

2. a=1.5x +b -> b=x+c => a=2.5x+c
now...we know for sure that x must be an even number...
suppose x=0
a=b=c -> it's possible, the question stem does not state that digits are different.

suppose x=2.
a=5+c
b=2+c

c can be 1 -> a=6, b=3
c can be 2 -> a=7, b=4.

so already 3 different options...definitely B alone is not sufficient.

answer is A.
Re: What is the three-digit number abc, given that a, b, and c   [#permalink] 01 Nov 2016, 05:51
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