Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 17 Jul 2019, 19:43

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

If A, B, and C are distinct positive digits and the product of the two

Author Message
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 56277
If A, B, and C are distinct positive digits and the product of the two  [#permalink]

Show Tags

14 Dec 2016, 05:52
00:00

Difficulty:

25% (medium)

Question Stats:

78% (01:52) correct 22% (02:24) wrong based on 136 sessions

HideShow timer Statistics

If A, B, and C are distinct positive digits and the product of the two-digit integers AB and AC is 156, what is the sum of the digits A, B, and C?

A. 4
B. 5
C. 6
D. 10
E. 25

_________________
Retired Moderator
Status: Long way to go!
Joined: 10 Oct 2016
Posts: 1344
Location: Viet Nam
Re: If A, B, and C are distinct positive digits and the product of the two  [#permalink]

Show Tags

14 Dec 2016, 10:24
1
2
Bunuel wrote:
If A, B, and C are distinct positive digits and the product of the two-digit integers AB and AC is 156, what is the sum of the digits A, B, and C?

A. 4
B. 5
C. 6
D. 10
E. 25

$$\overline{AB} \times \overline{AC}=156$$

We have $$(10A+B)(10A+C)=100A+10AB+10AC+BC=156$$

Since $$100A\leq 156 \implies A \leq 1 \implies A=1$$

Hence $$\overline{1B} \times \overline{1C}=156=12 \times 13$$

So $$B+C=2+3=5 \implies A+B+C=1+2+3=6$$

_________________
Manager
Joined: 18 Oct 2016
Posts: 139
Location: India
WE: Engineering (Energy and Utilities)
Re: If A, B, and C are distinct positive digits and the product of the two  [#permalink]

Show Tags

15 Dec 2016, 01:32
2
1
Option C)

Given: AB * AC = 156

: A + B + C = ?

$$156 = 2^2 * 3^1 * 13^1 = 4^1 * 3^1 * 13^1 = 12^1 * 13^1$$

Two numbers AB & AC have same 10's digit: As per above factorization it could only be 1, hence A = 1 and B & C = 2 & 3 or 3 & 2

We need not to get exact values of B & C, as in either case $$A + B + C = 1 + 2 + 3 = 1 + 3 + 2 = 6$$
_________________
Press Kudos if you liked the post!

VP
Joined: 07 Dec 2014
Posts: 1206
Re: If A, B, and C are distinct positive digits and the product of the two  [#permalink]

Show Tags

15 Dec 2016, 13:40
Bunuel wrote:
If A, B, and C are distinct positive digits and the product of the two-digit integers AB and AC is 156, what is the sum of the digits A, B, and C?

A. 4
B. 5
C. 6
D. 10
E. 25

the only two 2 digit factors of 156 are 12 and 13
1+2+3=6
C
Intern
Joined: 20 Dec 2017
Posts: 2
Re: If A, B, and C are distinct positive digits and the product of the two  [#permalink]

Show Tags

20 Dec 2017, 00:37
I would advise to do prime factorization of 156 = 2*78=2*2*39=2*2*3*13=12*13 so you get the two numbers and they are in the same format as mentioned i.e AB*AC . Thus you get respective values of A,B and C. Thus you get your answer quiet easily.
A+B+C=1+2+3=6
Re: If A, B, and C are distinct positive digits and the product of the two   [#permalink] 20 Dec 2017, 00:37
Display posts from previous: Sort by