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

 It is currently 21 Oct 2019, 13:28

### 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 = 8. Is ab > 8? (1) a^2 - b^2 = 32 (2) a^2 + b^2 = 40

Author Message
TAGS:

### Hide Tags

Manager
Joined: 13 Dec 2013
Posts: 144
Location: United States (NY)
Schools: Cambridge"19 (A)
GMAT 1: 710 Q46 V41
GMAT 2: 720 Q48 V40
GPA: 4
WE: Consulting (Consulting)
a + b = 8. Is ab > 8? (1) a^2 - b^2 = 32 (2) a^2 + b^2 = 40  [#permalink]

### Show Tags

09 Mar 2017, 17:15
1
4
00:00

Difficulty:

55% (hard)

Question Stats:

60% (01:57) correct 40% (02:09) wrong based on 81 sessions

### HideShow timer Statistics

a + b = 8. Is ab > 8?

(1) a^2 - b^2 = 32

(2) a^2 + b^2 = 40
VP
Joined: 05 Mar 2015
Posts: 1000
Re: a + b = 8. Is ab > 8? (1) a^2 - b^2 = 32 (2) a^2 + b^2 = 40  [#permalink]

### Show Tags

09 Mar 2017, 19:09
2
Cez005 wrote:
a + b = 8. Is ab > 8?

(1) a2 - b2 = 32

(2) a2 + b2 = 40

A. Statement (1) by itself is sufficient to answer the question, but statement (2) by itself is not.
B. Statement (2) by itself is sufficient to answer the question, but statement (1) by itself is not.
C. Statements (1) and (2) taken together are sufficient to answer the question, even though neither statement by itself is sufficient.
D. Either statement by itself is sufficient to answer the question.
E. Statements (1) and (2) taken together are not sufficient to answer the question.

Kudos if you like the q! Note a2 is equal to a squared and b2 is equal to b squared.

(1) a^2-b^2 = (a+b)(a-b)=32
putting a+b=8----------(x)
we get a-b= 32/8=4-------(y)
solving (x) & (y) we get definite values of a& b
thus we can find value ab
suff

(2) given a+b= 8
sq. both sides
a^2+b^2+2ab=64----(z)
but per option (2) a^2+b^2=40
substituting in eq(z) we get
2ab=64-40=24
thus ab=12
suff

Ans D
Manager
Joined: 13 Dec 2013
Posts: 144
Location: United States (NY)
Schools: Cambridge"19 (A)
GMAT 1: 710 Q46 V41
GMAT 2: 720 Q48 V40
GPA: 4
WE: Consulting (Consulting)
Re: a + b = 8. Is ab > 8? (1) a^2 - b^2 = 32 (2) a^2 + b^2 = 40  [#permalink]

### Show Tags

09 Mar 2017, 23:31
rohit8865 wrote:
Cez005 wrote:
a + b = 8. Is ab > 8?

(1) a2 - b2 = 32

(2) a2 + b2 = 40

A. Statement (1) by itself is sufficient to answer the question, but statement (2) by itself is not.
B. Statement (2) by itself is sufficient to answer the question, but statement (1) by itself is not.
C. Statements (1) and (2) taken together are sufficient to answer the question, even though neither statement by itself is sufficient.
D. Either statement by itself is sufficient to answer the question.
E. Statements (1) and (2) taken together are not sufficient to answer the question.

Kudos if you like the q! Note a2 is equal to a squared and b2 is equal to b squared.

(1) a^2-b^2 = (a+b)(a-b)=32
putting a+b=8----------(x)
we get a-b= 32/8=4-------(y)
solving (x) & (y) we get definite values of a& b
thus we can find value ab
suff

(2) given a+b= 8
sq. both sides
a^2+b^2+2ab=64----(z)
but per option (2) a^2+b^2=40
substituting in eq(z) we get
2ab=64-40=24
thus ab=12
suff

Ans D

a2 = (8-b)2 = 64-16b+b2, so 64-16b+b2+b2=40. Subbing into a2+b2=40:
24-16b+2b2=0
b2-8b+12=0
(b-2)(b-6)=0
b=2 or 6, both of which give answers of 6 and 2 for a respectively, therefore ab>8.
Director
Status: Come! Fall in Love with Learning!
Joined: 05 Jan 2017
Posts: 531
Location: India
Re: a + b = 8. Is ab > 8? (1) a^2 - b^2 = 32 (2) a^2 + b^2 = 40  [#permalink]

### Show Tags

10 Mar 2017, 01:21
1
a+b = 8
St 1: a^2 -b^2 = 32
or (a+b)(a-b) = 32
or 8(a-b) = 32
or a-b = 4 and a+b = 8. therefore a=6 and b=2. hence ab = 12 which is greater than 8.ANSWER

St 2: a^2+b^2 = 40
or(a+b)^2 - 2ab =40
or8^2 -2ab =40
or 2ab = 44 or ab =22 which is greater than 8. ANSWER

Option D
_________________
GMAT Mentors
Non-Human User
Joined: 09 Sep 2013
Posts: 13383
Re: a + b = 8. Is ab > 8? (1) a^2 - b^2 = 32 (2) a^2 + b^2 = 40  [#permalink]

### Show Tags

10 Apr 2019, 20:53
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: a + b = 8. Is ab > 8? (1) a^2 - b^2 = 32 (2) a^2 + b^2 = 40   [#permalink] 10 Apr 2019, 20:53
Display posts from previous: Sort by