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# ABA represents a three-digit number having digits A and B; BC3 represe

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Math Expert
Joined: 02 Sep 2009
Posts: 53020
ABA represents a three-digit number having digits A and B; BC3 represe  [#permalink]

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28 Jul 2017, 00:24
00:00

Difficulty:

95% (hard)

Question Stats:

37% (02:36) correct 63% (02:22) wrong based on 74 sessions

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ABA represents a three-digit number having digits A and B; BC3 represents another three digit number having digits B, C and 3. What is the value of B?

(1) ABA × 3 = BC3
(2) A, B, C and 3 are distinct non-zero digits.

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ABA represents a three-digit number having digits A and B; BC3 represe  [#permalink]

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Updated on: 28 Jul 2017, 07:00
Bunuel wrote:
ABA represents a three-digit number having digits A and B; BC3 represents another three digit number having digits B, C and 3. What is the value of B?

(1) ABA × 3 = BC3
(2) A, B, C and 3 are distinct non-zero digits.

(1) ABA * 3 = BC3

A*3 = 3

A can take only 1
ABA * 3 = BC3
101 * 3 = 303
111 * 3 = 333
121 * 3 = 363
131 * 3 = 393 B is 3
141 * 3 = 423 B is 4
151 * 3 = 453
161 * 3 = 483
171 * 3 = 513
181 * 3 = 543
191 * 3 = 573
Not sufficient

(2) Not Sufficient

On combining
We can say that B can only take 4 as A, B, C and 3 are distinct non-zero digits

C
P.S Corrected as i misread the second option
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Luckisnoexcuse

Originally posted by Luckisnoexcuse on 28 Jul 2017, 00:56.
Last edited by Luckisnoexcuse on 28 Jul 2017, 07:00, edited 1 time in total.
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Re: ABA represents a three-digit number having digits A and B; BC3 represe  [#permalink]

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28 Jul 2017, 06:37
In my opinion C.

(1) ABA * 3 = BC3

A*3 = 3

A can take only 1
ABA * 3 = BC3
101 * 3 = 303
111 * 3 = 333
121 * 3 = 363
131 * 3 = 393 B is 3
141 * 3 = 423 B is 4
151 * 3 = 453
161 * 3 = 483
171 * 3 = 513
181 * 3 = 543
191 * 3 = 573
Not sufficient

(2) Not Sufficient

On combining
A=1, B=(3,4), C= (2,9) and 3 are distinct non-zero integers. As 3 is already an integer, b cannot take the value of 3, so b must be 4.

C
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Re: ABA represents a three-digit number having digits A and B; BC3 represe  [#permalink]

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17 Dec 2017, 14:36
Hi All,

This DS question is built around a few Number Property rules, but even if you don't spot those pattern you can still get the correct answer with a little 'brute force' arithmetic.

We're told that A, B and C are DIGITS in the three-digit numbers ABA and BC3. This means that each of those variables can only be the numbers 0-9 inclusive. We're asked for the value of B.

1 )ABA x 3 = BC3

There are only 10 possible values for A - and Fact 1 gives us an equation that tells us that when we multiply A by 3, we get a number that ENDS in a 3. Could A = 5? NO - because multiplying a number that ends in 5 by 3 will gives us a number that ends in a 5. How long would it take you to multiply each possible digit by 3 and see what happens? You'll find that there's just ONE possibility that 'fits'... A = 1. With that value 'locked in', we have...

1B1 x 3 = BC3

From here, we can take the same approach to figure out the possible value(s) of B. Could B = 1? NO - because 111 x 3 = 333 (not 1C3). How long would it take to work through the other possibilities (hint: you won't have to work for very long). You'll find that B = 3 and B = 4 are both possibilities.

131 x 3 = 393
141 x 3 = 423
Fact 1 is INSUFFICIENT.

2) A, B, and C are distinct non-zero digits.

Fact 2 lets us know that the three variables are all different from one another, but there's still no way to determine the exact value of B.
Fact 2 is INSUFFICIENT.

Combined, we still end up with two possible outcomes (A=1, B=3, C=9 and A=1, B=4, C=3).
Combined, INSUFFICIENT.

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Rich
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Re: ABA represents a three-digit number having digits A and B; BC3 represe   [#permalink] 17 Dec 2017, 14:36
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