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

 It is currently 18 Oct 2018, 03:03

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

M27-08

Author Message
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 49992

Show Tags

16 Sep 2014, 01:27
13
00:00

Difficulty:

(N/A)

Question Stats:

33% (01:40) correct 67% (01:52) wrong based on 192 sessions

HideShow timer Statistics

The product of three distinct positive integers is equal to the square of the largest of the three numbers, what is the product of the two smaller numbers?

(1) The average (arithmetic mean) of the three numbers is $$\frac{34}{3}$$.

(2) The largest number of the three distinct numbers is 24.

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 49992

Show Tags

16 Sep 2014, 01:27
4
3
Official Solution:

This is a 700 question.

Let the three integers be $$a$$, $$b$$, and $$c$$, where $$0 \lt a \lt b \lt c$$. Given: $$abc=c^2$$ so, $$ab=c$$. Question: $$ab=c=?$$

(1) The average (arithmetic mean) of the three numbers is $$\frac{34}{3}$$. This basically means that $$a+b+c=34$$. Substitute the value of $$c$$ with $$ab$$ to get $$a+b+ab=34$$. From that we can write $$(a+1)(b+1)=35$$. Now, since $$a$$ and $$b$$ are integers, then $$a+1=5$$ and $$b+1=7$$. $$a=4$$ and $$b=6$$, hence $$ab=24$$. Sufficient. (Notice that $$a+1=1$$ and $$b+1=35$$ is not possible since in this case $$a=0$$ and we are told that all integers are positive).

(2) The largest number of the three distinct numbers is 24. Directly gives the value of $$c$$. Sufficient.

_________________
Intern
Joined: 16 Jun 2015
Posts: 6

Show Tags

10 Aug 2015, 18:37
1
Bunuel,

How did you get from a+b+ab=34 to (a+1)(b+1)=35?

Tks,
Verbal Forum Moderator
Joined: 15 Apr 2013
Posts: 184
Location: India
Concentration: General Management, Marketing
GMAT Date: 11-23-2015
GPA: 3.6
WE: Science (Other)

Show Tags

23 Aug 2015, 04:41
5
Hello,

a + b + ab = 34

a + b+ ab + 1 =34+1

a(1+b) + (b+1) = 35

(b+1) (a + 1) =35

Hope it helps.

Press kudos please if it helps!
Intern
Joined: 10 Jun 2017
Posts: 23

Show Tags

26 Apr 2018, 02:22
I didn't get the part in which you go from:

a(1+b) + b + 1 = 35

to

(a+1)(b+1) = 35

Could you please elaborate just a lil more?

Thanks a lot!

cheers to y'aal!
Math Expert
Joined: 02 Sep 2009
Posts: 49992

Show Tags

26 Apr 2018, 02:31
Miracles86 wrote:
I didn't get the part in which you go from:

a(1+b) + b + 1 = 35

to

(a+1)(b+1) = 35

Could you please elaborate just a lil more?

Thanks a lot!

cheers to y'aal!

Factor out b + 1 our of a(b + 1) + (b + 1) = 35 to get (b + 1)(a + 1) = 35.
_________________
Intern
Joined: 10 Jun 2017
Posts: 23

Show Tags

26 Apr 2018, 02:33
Obviously.... silly me!

Thanks
Intern
Joined: 12 Aug 2018
Posts: 1

Show Tags

18 Sep 2018, 07:39
Quote:
(2) The largest number of the three distinct numbers is 24. Directly gives the value of cc. Sufficient.

With #2 alone, c*x = 576, which means a*b = 24, there are two solutions with distinct positive integers.

a = 3, b=8, c=24
a*b*c = 3*8*24 = 576 = 24^2

a = 4, b=6, c=24
a*b*c = 4*6*24 = 576 = 24^2

Using the information from 1), we know that a=3, b=8 is not correct. However, I don't see how we would know this from 2) alone.

Intern
Joined: 22 Nov 2016
Posts: 3

Show Tags

18 Sep 2018, 09:04
I also have the same query as Double down.kindly explain.Or is it because we are asked only abt ab?

Posted from my mobile device
Math Expert
Joined: 02 Sep 2009
Posts: 49992

Show Tags

18 Sep 2018, 09:07
monicasharma365 wrote:
I also have the same query as Double down.kindly explain.Or is it because we are asked only abt ab?

Posted from my mobile device

Yes.

The product of three distinct positive integers is equal to the square of the largest of the three numbers, what is the product of the two smaller numbers?
_________________
Intern
Joined: 24 Dec 2011
Posts: 11
Location: India
GPA: 4
WE: General Management (Health Care)

Show Tags

18 Sep 2018, 10:27
the question stem says three distinct positive integers and the product is equal to the square of the highest no.
which means the product is equal to the highest number.

lets say abc, c being the highest no.
a*b*c= c^2
which implies ab=c

first choice explanation
a+b+c=34
a+b+c+1=34+1
we know ab=c
a+b+ab+1=35
a+ab+b+=35
a(1+b) + (1+b)=35
taking (1+b) out
(1+b)(1+a)=35
factors of 35=1,5,7,35
(1,35) cannot be the pair as a or b is a positive integer
(5,7) is the pair
which means (4,6) is a pair for (a,b)

hence the product is 24
M27-08 &nbs [#permalink] 18 Sep 2018, 10:27
Display posts from previous: Sort by

M27-08

Moderators: chetan2u, Bunuel

 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®.