It is currently 23 Jun 2017, 10:42

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# For integers, a and b, if sqrt ( a^3 - a^2 - b) = 7, what is

Author Message
Director
Joined: 23 Jun 2005
Posts: 841
GMAT 1: 740 Q48 V42
For integers, a and b, if sqrt ( a^3 - a^2 - b) = 7, what is [#permalink]

### Show Tags

24 Oct 2006, 13:53
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

### HideShow timer Statistics

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

For integers, a and b, if sqrt ( a^3 - a^2 - b) = 7, what is the value of a?

1. a^2 - a = 12
2. b^2 - b = 2

(Edit: Added the original question for clarity.)
Attachments

Princeton T2 Q32.jpg [ 9.78 KiB | Viewed 648 times ]

Last edited by anandsebastin on 24 Oct 2006, 14:36, edited 1 time in total.
Manager
Joined: 01 Oct 2006
Posts: 242
Re: DS: Value of a [#permalink]

### Show Tags

24 Oct 2006, 14:09
I get C.

From 1, a = 4 or -3
From 2, b = 2 or -1.

sqrt ( a^3 - a^2 - b) = 7 is satisfied only by a = 4 and b = -1
SVP
Joined: 01 May 2006
Posts: 1796

### Show Tags

24 Oct 2006, 14:15
for me (C)

sqrt ( a^3 - a^2 - b) = 7
=> a^3 - a^2 - b = 49 (1)

Stat 1 :

a^2 - a = 12
<=> a^2 - a - 12 = 0
<=> (a+3)(a-4) = 0
<=> a = -3 or a = 4

Both values of a work in (1)

INSUFF

Stat 2 :

b^2 - b = 2
<=> b^2 - b - 2 = 0
<=> (b-2)*(b+1) = 0
<=> b=2 or b=-1

Placed in (1), we have several possible values of a

INSUFF

Combining (1) with (2):

case 1 : a = -3
(1) => (-3)^3 - (-3)^2 -b = 49
<=> -36 - b = 49
<=> b = -85 >>> Not matching values of b in statment 2

case 2 : a = 4
(1) => (4)^3 - (4)^2 -b = 49
<=> 64 - 16 - b = 49
<=> b = 48-49 = -1 >>> Bingo 1 match with 1 value of b in statment 2
Intern
Joined: 25 Sep 2006
Posts: 23
Re: DS: Value of a [#permalink]

### Show Tags

25 Oct 2006, 11:42
anandsebastin wrote:
For integers, a and b, if sqrt ( a^3 - a^2 - b) = 7, what is the value of a?

1. a^2 - a = 12
2. b^2 - b = 2

B
as mst and fig have calculated
from stat 2, b = 2 or b=-1

from stem a^3-a^2-b=49
hence a^3-a^2 = 49+b
a*a*(a-1) = 49+b

if b = 2
a*a*(a-1) = 51
but 51 = 17*3 and neither of them can be used as a in equation above (and we have to find integer a)

if b=-1
a*a*(a-1) = 48

factoring 48, it is possible to get
48 = 4*4*3
hence a=4

from stat 1, a=4 or a=-3
both can be used to satisfy the stem equation and arrive at different solutions for b as b = a*a*(a-1) -49 where b= -1 or b=-85
Manager
Joined: 04 May 2006
Posts: 172
Location: paris

### Show Tags

25 Oct 2006, 13:38
I'm getting B as well
the only option for a and b to be integers is if a=4 and b=-1
_________________

time is not on my side

SVP
Joined: 01 May 2006
Posts: 1796

### Show Tags

25 Oct 2006, 13:55
Yesss ..... It's (B)

This is my favorite silly mistake : to forget that we are speaking about integers. As a is in integer, there is only 1 possible solution with the statment 2

Thanks guys :D
Director
Joined: 23 Jun 2005
Posts: 841
GMAT 1: 740 Q48 V42

### Show Tags

25 Oct 2006, 18:38
Muddypaws nailed it.

OA is B. The explanation was scrambled in Princeton Review.
25 Oct 2006, 18:38
Display posts from previous: Sort by