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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.

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.

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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16 Oct 2013, 06:26

(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.

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

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28 Oct 2014, 08:01

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

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06 Oct 2015, 14:15

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.

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

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21 Sep 2016, 11:42

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

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

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01 Nov 2016, 06:51

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.

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