GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 24 May 2019, 09:14

### 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

# a, b, and c are integers such that ab + c = 7, ac + b = 5, and a + b +

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 55271
a, b, and c are integers such that ab + c = 7, ac + b = 5, and a + b +  [#permalink]

### Show Tags

05 Jul 2018, 04:41
1
4
00:00

Difficulty:

45% (medium)

Question Stats:

70% (02:21) correct 30% (02:37) wrong based on 43 sessions

### HideShow timer Statistics

a, b, and c are integers such that ab + c = 7, ac + b = 5, and a + b + c = 6. What is the value of abc ?

A. 2
B. 6
C. 9
D. 12
E. 18

_________________
Manager
Joined: 20 Apr 2018
Posts: 173
Concentration: Technology, Nonprofit
WE: Analyst (Non-Profit and Government)
Re: a, b, and c are integers such that ab + c = 7, ac + b = 5, and a + b +  [#permalink]

### Show Tags

05 Jul 2018, 04:59
1
Given:
ab + c = 7 -- (eq. 1)
ac + b = 5 -- (eq. 2)
a + b + c = 6 -- (eq. 3)

Add eq. 1 and 2
(a+1)(b+c) = 12
Substitute b+c = 6 - a from eq. 3
(a+1)(6-a) = 12
This gives a = 2, 3

Pick a value. Say a = 3
Substitute in eq. 1 and 2
3b + c = 7
3c + b = 5
==> b = 2 and c = 1
a*b*c = 3*2*1 = 6

Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3386
Location: India
GPA: 3.12
Re: a, b, and c are integers such that ab + c = 7, ac + b = 5, and a + b +  [#permalink]

### Show Tags

05 Jul 2018, 05:12
Bunuel wrote:
a, b, and c are integers such that ab + c = 7, ac + b = 5, and a + b + c = 6. What is the value of abc ?

A. 2
B. 6
C. 9
D. 12
E. 18

Going from the answer options can be advantageous in this kind of problem.

A. 2 = 2*1 | a = 2,b = c = 1
Whichever way we go about the numbers, we can't get a sum s.t a + b + c = 6

B. 6 = 2*3 | a = 2,b = 3,c = 1
In this case a + b + c = 6. Also, ab + c = 6 +1 = 7 and ac + b = 2 + 3 = 5.

Therefore, Option B(6) is the value of abc.
_________________
You've got what it takes, but it will take everything you've got
Manager
Joined: 12 Sep 2017
Posts: 246
a, b, and c are integers such that ab + c = 7, ac + b = 5, and a + b +  [#permalink]

### Show Tags

16 Mar 2019, 15:40
Given...

ab + c = 7... c = 7 - ab
ac + b = 5... b = 5 - ac
a + b + c = 6

From the third eq...

a + 5 - ac + 7 - ab = 6

$$c + b = \frac{6+a}{a}$$

So from a + b + c = 6

$$a^2 - 5a + 6 =0$$
$$(a-2)(a-3)$$

If A1 = 2 then b +c could be (2,2) and (3,1)
If A2 = 3 then b + c could be (2,1)

abc...

(1)(2)(2) = 8 or (2)(3)(1) = 6 (A1)
(3)(2)(1) = 6 (A2)

B
a, b, and c are integers such that ab + c = 7, ac + b = 5, and a + b +   [#permalink] 16 Mar 2019, 15:40
Display posts from previous: Sort by

# a, b, and c are integers such that ab + c = 7, ac + b = 5, and a + b +

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.