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If the three-digit integer x=”abc”, where a, b, and c

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If the three-digit integer x=”abc”, where a, b, and c [#permalink] New post 04 May 2012, 06:21
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If the three-digit integer x=”abc”, where a, b, and c represent nonzero digits of x, what is the value of x?

(1) a>= 3b
(2) b>= 3c
[Reveal] Spoiler: OA
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Re: If the three-digit integer x=”abc”, where a, b, and c [#permalink] New post 04 May 2012, 07:55
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If the three-digit integer x=”abc”, where a, b, and c represent nonzero digits of x, what is the value of x?

(1) a>= 3b. Not sufficient, since no info about c.
(2) b>= 3c. Not sufficient, since no info about a.

(1)+(2) We have that a>= 3b and b>= 3c. Now, since each represent a nonzero single digit then c can only be 1, b can only be 3 and a can only be 9. Because if c=2 (or more) then the least value of b is 6 and in this case the least value of a is 18, so it's no more a single digit. Sufficient.

Answer: C.

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Hope it helps.
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Re: If the three-digit integer x=”abc”, where a, b, and c [#permalink] New post 06 May 2012, 15:20
Will vote for C

(A) a >= 3b

if (b = 1)

a = {3,4,5 ...}

not sufficient

(B) b >= 3c


if (c = 1)
b = {3,4,5 ....}

(C)

if (c = 1)

b = 3 and a = 3b = 3 * 3 = 9

and therefore sufficient

b cannot be > 3, if b = 4 then a will be 12 (not a digit)
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Re: If the three-digit integer x=”abc”, where a, b, and c [#permalink] New post 21 Jan 2014, 14:22
If the three-digit integer x=”abc”, where a, b, and c represent nonzero digits of x, what is the value of x?

(1) a>= 3b
Insufficient. a<= 9
(2) b>= 3c
Insufficient b<= 9

1+2) If we combine both inequalities together we end up with a/3>=b>=3c, thus the only values a can assume are 3 and 9, if a=3 the inequality does not hold true. Pick a=9 at this point we must minimize c, which will be 1, and b will be 3. Thus the value of abc is 931.

Otherwise you can solve it by plugging in numbers.

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Re: If the three-digit integer x=”abc”, where a, b, and c   [#permalink] 21 Jan 2014, 14:22
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