The numbers a, b, and c are all positive. If b^2 - c^2 = 17, then wha

Question

The numbers a, b, and c are all positive. If b^2 - c^2 = 17, then what is the value of a^2 - c^2?

(1) a – b = 3
(2) (a + b)/(a - b)= 7

RAHULSAINI · Answer

Answer is C

Statement 1 : a-b=3 so b=a-3 and b^2 = a^2+9-6a substituting in given eq we get a^2-c^2=17-9+6a

Statement 2 : a+b/a-b= 7 on solving and substituting in given equation we get c^2=9/16a^2-17 so not sufficient

(1)+(2)

On solving together we get two values of a = 12 b = 9 so a^2-C^2=144-64

so C

Got Confused while combining 1 and 2 first time so edited

ravihanda · Answer

We are given that b^2 - c^2 = 17
We are asked to find out the value of (a^2 - c^2)

Statement 1 says (a - b) = 3
=> a = b + 3
=> a^2 - c^2 = b^2 + 6b + 9 - c^2 = 17 + 6b + 9
This statement alone is not sufficient.

Statement 2 says (a + b)/(a - b) = 7
=> a + b = 7a - 7b
=> 8b = 6a
=> a = 4b/3
=> a^2 - c^2 = 16b^2/9 - c^2 = 7b^2/9 +17
This statement alone is not sufficient.

When we combine the two we get
a = b + 3 and a = 4b/3
=> 4b/3 = b + 3
=> b = 9
=> a = b + 3 = 12
=> c = sqrt(b^2 - 17) = sqrt(81 - 17) = sqrt(64) = 8
=> a^2 - c^2 = 12^2 - 8^2 = 80.

So, we have found out the answer by using both the statements together. 
 Correct answer option : C

ynaikavde · Answer

(a+b)(a-b)=17

both statements don't get us close to the value of C
in order to get value of c we have to know value of A or B for that we can use both statements and get value of A and B to get value of C

b^2-c^2=17>>(a-3)^2-c^2=17 
and a+b=21
a=12,b=9 
with this we get c=+-8 we know they are positive so 8

hence answer is C

CrackverbalGMAT · Answer

Hi ,
(b+c)(b-c)=17, what is the value of (a+c)(a-c)?
Statement 1 is insufficient:
 This does not say anything c. Also a-b=3 will have many values for a and b.
Statement 2 is also insufficient:
This again does not say anything about c. Also (a + b)/(a - b)= 7 has many values.
Together sufficient:
(a+b)=21 and a-b=3
Solving we get a=12 and b=9
If we subs in b^2 - c^2 = 17 we get c^2=8. 
So we know values of a and c.
So together sufficient.
Answer is C.

nphatak · Answer

I think the answer should be D. b^2-c^2 = 17, leaves us with two b = 9 and C = 8. These are the only two possible positive numbers whose squares differ by 17. 
a. Substituting for b, we get a, and hence sufficient.
b. Again substituting for b, we get the value for A. Sufficient.

EMPOWERgmatRichC · Answer

Hi nphatak,

The prompt does NOT state that A, B and C are integers. Knowing that they might be non-integers, are there any OTHER values that you can come up with for B and C.....?

GMAT assassins aren't born, they're made,
Rich

Bunuel · Answer

MAGOOSH OFFICIAL SOLUTION:

Let X = a^2 - c^2, the value we are seeking. Notice if we subtract the first equation in the prompt from this equation, we get a^2 - b^2 = X – 17. In other words, if we could find the value of a^2 - b^2, then we could find the value of X.

Statement #1: a – b = 3

From this statement alone, we cannot calculate a^2 - b^2, so we can’t find the value of X. Statement #1, alone and by itself, is insufficient.

Statement #2: (a + b)/(a - b) = 7

From this statement alone, we cannot calculate a^2 - b^2, so we can’t find the value of X. Statement #2, alone and by itself, is insufficient.

Statements #1 & #2 combined: Now, if we know both statements are true, then we could multiple these two equations, which cancel the denominator, and result in the simple equation a + b = 21. Now, we have the numerical value of both (a – b) and (a + b), so from the difference of two squares formula, we can figure out a^2 - b^2, and if we know the numerical value of that, we can calculate X and answer the prompt. Combined, the statements are sufficient.

Answer = C

23a2012 · Answer

Dear , can you I tried to find examples for A,B as non-integer numbers in form (A+B)(A-B)=17 but i did not found?

can you give me examples

chetan2u · Answer

Dear , can you I tried to find examples for A,B as non-integer numbers in form (A+B)(A-B)=17 but i did not found?

can you give me examples

hi  23a2012 
you can have lot of examples ...
let  a+b=17/2.. a-b=2...  so (a+b)(a-b)=2*17/2=17..
there are two numbers a and b and two eq, so u can find the answer..
a+b=17/2.. 
a-b=2 or a=b+2.
put the value in above equation..
b+2+b=17/2.. 
2*b=17/2 - 2 = 13/2.... so b = 13/4 and a= b+2=13/4+2=21/4....
similarly a+b=17/3.. a-b=3... and so on

renept · Answer

Hi Bunuel,
I don't know why I don't get the highlighted part above. I get the arithmetic behind it but fail to understand why we can do this. I am familiar with systems of equations where you add and subtract equations to eliminate terms. I have a feeling this is very simple but I am just not seeing it. Please help! 
Thanks

EMPOWERgmatRichC · Answer

Hi renept,

I think that you might find it easier to think of that math as 'substitution' instead of multiplication.

Fact 1 tells us that (a - b) = 3
Fact 2 gives us another equation: (a + b)/(a - b) = 7

Combining the two Facts, notice how (a - b) appears in both equations? We can 'substitute' the value of (a - b) into the second equation, which would give us...

(a + b)/3 = 7
(a + b) = 21

GMAT assassins aren't born, they're made,
Rich

Crytiocanalyst · Answer

(1) a – b = 3
3 variable 2 eqn not possible to solve 
Clearly insufficient

(2) (a + b)/(a - b)= 7
 3 variable 2 equation not possible

However when 1 and 2 is combined 3 variables 3 equation possible to solve

Therefore IMO D

Arihant16 · Answer

The equation (B^2 - C^2 = 17) can be factored as ((B + C)(B - C) = 17). The possible factor pairs for 17 are ((1, 17)) and ((-1, -17)), since 17 is a prime number. This leads to the following possibility:

(B + C = 17) and (B - C = 1)
 Solving these two equations simultaneously, we get (B = 9) and (C = 8)

HENCE Now we can solve for A and the answer is {b}Option D 
 Bunuel   EMPOWERgmatRichC  help!!!!!!!!!!

Bunuel · Answer

We are not give that a, b, and c are integers, hence your reasoning in red above is not correct.

EMPOWERgmatRichC · Answer

Hi Arihant16, This exact issue is discussed in older posts further up the thread, but to reiterate: While the prompt does tell us that A, B and C are POSITIVE, it does NOT state that the three variables are integers. Thus, while B=9, C=8 is a possible solution to the given equation, it is NOT the only one. GMAT assassins aren't born, they're made, Rich Contact Rich at: Rich.C@empowergmat.com www.empowergmat.com

VivekSri · Answer

----------------------------------------------
Since A,B,C are all positive and not the integer, We can also give B=5 and C=2 \sqrt{2}  then also your answer might come, Since it is just a number not integer, you cant give this as answer

The numbers a, b, and c are all positive. If b^2 - c^2 = 17, then wha

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

The numbers a, b, and c are all positive. If b^2 - c^2 = 17, then wha

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards