What is the value of p? (1) 4|q^2 - 1| = p - 5 (2) |7 - p| = 6

Question

Competition Mode Question

What is the value of p?

(1)  4|q^2 - 1| = p - 5

(2)  |7 - p| = 6

Are You Up For the Challenge: 700 Level Questions

MayankSingh · Answer

IMO E

Statement 1:   
 4|q^2-1| = p-5
if q^2>1 : 4(q^2-1)= p-5
if q^2<1 : -4(q^2-1)= p-5
We have two variables and one equation.

Not Sufficient.

Statement 2:   
 |7-p| = 6
(7-p) = +/-6
p= 7 +/- 6
p= 13 0r 1
 
 Not Sufficient

Together  :  We have no idea of q, so still value of p cannot be determined ...  Not Sufficient.

ArunSharma12 · Answer

statement 1: 4|q^2−1|=p−5 case 1: q^2 < 1 -4q^2 + 4 = p -5 p = 9 - 4q^2 case 2: q^2 > 1 4q^2 - 4 = p -5 p = 1 + 4q^2 not sufficient statement 2: |7−p|=6 7 - p = 6; p =1 | p -7 = 6; p =13 p can be (1,13) not sufficient combining both statements, case 1: q^2 < 1 4q^2 = 9 - p when p = 1: q^2 = 2 (no value of q possible) when p = 13: q^2 = -ve value (not possible) case 2: q^2 > 1 p = 1 + 4q^2 4q^2 = p -1 when p = 1: q^2 = 0 (no value of q possible) when p = 13: q^2 = 3 (possible) p =13 ans: C

Babineaux · Answer

IMO ans is C.

Let me take the 2nd Statement first,

|7-p| = 6 
by solving we get p = 1 or 13.
Thus insufficient.

Now coming to 1st Statement,
4|q^2-1| = p-5
Here we are having two unknown variables, thus insufficient

Combining both statements,
Putting p = 1 in statement 2, we get RHS as -ve 
now for any set of values of q, we can conclude RHS will always be +ve 
Hence we can say that p=13 and not 1.

Thus IMO ans is C.

nick1816 · Answer

Statement 1-  From this equation, obviously we can't find the value of p, as q is unknown. But this statement gives us the range of p.

p ≥ 5

Insufficient

Statement 2-  p can be 1 or 13

Insufficient

Combining both statements

Since p ≥ 5  (from statement 1) ,

p=13   (from statement 2)

Sufficient

sambitspm · Answer

Kindly see the attachment
C

NiftyNiffler · Answer

What is the value of p?

(1) 4|q2−1|=p−5

(2) |7−p|=6

In statement 1, there are 2 unknown variables. We can't get definitive value of p . 
p - 5 >= 0
=> p >= 5 (INSUFFICIENT)

St2: |7-p| = 6

So, p = 1 or 13 (INSUFFICIENT)

Both taken together, p = 13 (SUFFICIENT)

Hence, the answer is  C

chetan2u · Answer

What is the value of p?

(1)  4|q^2 - 1| = p - 5 
We cannot find p as there is another variable q. But it does tell us that  p-5\geq{0}  because  4|q^2-1|  will never be less than 0.
 p-5\geq{0} ..... p\geq{5}

(2)  |7 - p| = 6 
two cases -
a)  7-p=6......p=7-6=1 
b)  p-7=6......p=7+6=13

Combined..
 p\geq{5} , so  p=13

C

Saasingh · Answer

E?

(1) here we have equation in two variables so impossible to find P.

Not sufficient.

(2) Given the mod , we get two equations: 
--> 7-p = 6 and 
--> p-7 = 6

Thus we get two values of P i.e. 1 and 13 which isn't unique.

Even when we combine (1) and (2), we get no new information.

Thus, E

Posted from my mobile device

exc4libur · Answer

(1) insufic
p=4|q^2-1|+5
p=4|≥0|+5
p≥5

(2) insufic
pos case: 7-p=6, p=1
neg case: 7-p=-6, p=13

(1/2) sufic
p=13

Ans (C)

Abi1995 · Answer

Ans - E

Statement-1 
Cannot give one value of P as Q can be + or - , value of p will change accordingly 
Not sufficient

Statement 2 - 
By solving this we get 2 values of p = 8 or 1 , again not sufficient

Combining 1 and 2 will still not give single value of p , so this is again insufficient

Posted from my mobile device

bumpbot · Answer

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.

What is the value of p? (1) 4|q^2 - 1| = p - 5 (2) |7 - p| = 6

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

What is the value of p? (1) 4|q^2 - 1| = p - 5 (2) |7 - p| = 6

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