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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]  04 May 2012, 07:21
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91% (01:53) correct 8% (02:00) wrong based on 35 sessions
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
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Re: If the three-digit integer x=”abc”, where a, b, and c [#permalink]  04 May 2012, 08:55
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.

Similar questions to practice:
if-x-0-abcd-where-a-b-c-and-d-each-represent-a-nonzero-127399.html
if-x-0-rstu-where-r-s-t-and-u-each-represent-a-nonzero-109735.html

Hope it helps.
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Re: If the three-digit integer x=”abc”, where a, b, and c [#permalink]  06 May 2012, 16:20
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)
Re: If the three-digit integer x=”abc”, where a, b, and c   [#permalink] 06 May 2012, 16:20
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