If P and Q are integers and P^Q = 16, what is the value of |P - Q| ?

Question

Competition Mode Question

(1) Q ≠ 1
(2) P > 0

shameekv1989 · Answer

If P and Q are integers and P^Q = 16, what is the value of |P - Q| ?

(1) Q ≠ 1
(2) P > 0

For  P^Q= 16  -> P=2, Q=4; P=4 Q=2; P=16, Q=1; P=-2, Q=4; P=-4, Q=2 -> |P-Q| = 2,2,15,6,6 respectively

i) Q is not equal to 1 -> |P-Q| can be 2 or 6 - Not sufficient
ii) P>0 -> P=2, Q=4; P=4,Q=2; P=16 Q=1 -> |P-Q| = 2,2,15 -> Not Sufficient

Combining i) and ii)

Only possible values are P=2 Q=4; P=4, Q=2 -> |P-Q| = 2 -> Hence Sufficient

Answer - C

GMATinsight · Answer

SOlution :
P^Q = 16 = 2^4 = 4^2 = 16^1

i.e. 
Case 1:  p  =  + 2, Q = 4 and |P - Q| = | + 2 - 4| = 2 or 6
Case 2:  p  =  + 4, Q = 2 and |P - Q| = | + 4 - 2| = 2 or 6
Case 3:  p  = 16, Q = 1 and |P - Q| = |16 - 1| = 15

Question : |P - Q| = ?

Statement 1 : Q≠1

i.e. Case 3 is OUT and Case 1 and Case 2 both give |P - Q|=2 or 6 hence

NOT SUFFICIENT

Statement 2 : P > 0

We still have values of |P - Q| as 2 or 6

NOT SUFFICIENT

Combining

After combining |P - Q| as 2 for positive values of P (Case 1 and 2)

SUFFICIENT

Answer: Option C

Archit3110 · Answer

#1
Q ≠ 1
we P =2 , q=4 ; or p=2 ,q=4 or p=-4 q=2 
|P - Q| = 2, 6 insufficient
#2
P > 0
P = 2,4,16 and q = 4,2,1 again insufficient
from 1 &2
|P - Q| = 2
IMO C; sufficient

If P and Q are integers and P^Q = 16, what is the value of |P - Q| ?

(1) Q ≠ 1
(2) P > 0

rajatchopra1994 · Answer

Given: P^Q = 16, Need to find |P - Q|

Statement 1:Q ≠ 1
P,Q value can be (-4,2), (2,4) & (4,2).
So it will give 2 values for |P - Q| = 6, 2 
Not Sufficient.
Statement 2: P>1
P,Q value can be (16,1), (2,4) & (4,2).
So it will give 2 values for |P - Q| = 15, 2 
Not Sufficient.

Combining 1&2,
P,Q value can be (2,4) & (4,2).
So it will give 1 values for |P - Q| = 2 
Sufficient.

IMO-C

GMATWhizTeam · Answer

Solution 
 Step 1: Analyse Question Stem 
 •  P  and  Q  are integers.
 o  P^Q = 16  
• If  P = 16 , and  Q = 1 , then  P^Q=16 
 o  |P-Q|=15  
• If  P = 4 , and  Q = 2 , then  P^Q=16 
 o  |P-Q|=2  
• If  P = -4 , and  Q = 2 , then  P^Q=16 
 o  |P-Q|=6  
• If  P = 2 , and  Q = 4 , then  P^Q=16 
 o  |P-Q|=2  
• If  P = -2 , and  Q = 4 , then  P^Q=16 
 o  |P-Q|=6   
 Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE 
Statement 1: 
 • It means  Q  can either be  2  or  4 ,
 o Here, multiple cases are possible and the value  |P-Q|  for each case is different.  
Hence, statement 1 is not sufficient, we can eliminate answer options B, C, and E.
Statement 2: 
 • It means  p  can either be  2, 4  or  16 .
 o Here, multiple cases are possible and the value  |P-Q|  for each case is different.  
Hence, statement 2 is also not sufficient, we can eliminate option B.
 Step 3: Analyse Statements by combining. 
From equation 1: Q can be either  2  or  4 
From equation 2: P can be either  2, 4 , or  16 
By combining the both there are two possible cases.
 • Case 1: If  p = 4  and  Q = 2 , then  |P-Q|=2 .
• Case 2: If  P = 2  and  Q = 4 , then  |P-Q|=2 . 
Hence, the correct answer is Option C.

exc4libur · Answer

PˆQ=16 (both integers)
P,Q: 2ˆ4, -2ˆ4, 4ˆ2, -4ˆ2, 16ˆ1

(1) Q ≠ 1   insufic

q=4,2
p=2,-2,4,-4
|p-q|: 2-4=-2=2, -2-4=-6=6, -4-2=-6=6, 4-2=2

(2) P > 0   insufic

p=2,4,16
q=4,2,1
|p-q|: 2-4=-2=2, 4-2=2, 16-1=15

(1&2)   sufic

p=2,4
q=4,2
|p-q|: 2-4=-2=2, 4-2=2,

Ans (C)

firas92 · Answer

If P and Q are integers and P^Q = 16, what is the value of |P - Q| ?

(1) Q ≠ 1

If P=2, Q=4, |P-Q|=2
If P=-4, Q=2, |P-Q|=6

Not Sufficient

(2) P > 0

If P=16, Q=1, |P-Q|=15
If P=2, Q=4, |P-Q|=2

Not Sufficient

(1)+(2)

Either P=2, Q=4 or P=4, Q=2

In both cases |P-Q|=2

Sufficient

Answer is (C)

suchita2409 · Answer

IMO A.

If q!=1 then we have 2^4 =16
4^2 =16 Resulting answer to be 2 in both cases. Hence sufficient.

Stmt 2 says p greater than 0 can be 16,4,2 can have resulting answer to be 2 or 15
Insufficient
.

Posted from my mobile device

ostrick5465 · Answer

If P and Q are integers and P^Q = 16, what is the value of |P - Q|?

(1) Q ≠ 1
(2) P > 0

(1) Q ≠ 1 => P = -4; Q = 2 or P = 4; Q = 2
=> Not Suff

(2) P > 0 => P = 16; Q = 1 or P = 4; Q = 2
=> Not Suff

Combine (1) & (2) => P = 4; Q = 2
=> Suff

=>  Choice C

Jawad001 · Answer

If P and Q are integers and P^Q = 16, what is the value of |P - Q| ?

(1) Q ≠ 1
(2) P > 0
Conditions: 
• P and Q are integers
• P^Q = 16

First cases:
 (I) Let p = -4 and Q = 2, then P^Q = (-4) ^2 = 16
 Therefore, |P- Q | = |-4- 2 |= |-6 |= 6
 (II) P = 4 and Q = 2, then P^Q = (4) ^2 = 16
 Therefore, |P- Q | = |4- 2 |= |2 |= 2
 (III) P = 2 and Q = 4, then P^Q = (2) ^4 = 16
 Therefore, |P- Q | = |2- 4 |= |-2 |= 2
Therefore, statement (1) is not sufficient.

Second cases:
(I) Let p = 2 and Q = 4, then P^Q = (2) ^4 = 16
 Therefore, |P - Q| = |2- 4 |= |-2 |= 2
(II) P = 4 and Q = 2, then P^Q = (4) ^2 = 16
 Therefore, |P- Q | = |4- 2 |= |2 |= 2
(III P = 16 and Q = 1, then P^Q = (16) ^1 = 16
 Therefore, |P- Q | = |16- 1 |= |15 |= 15
Therefore, statement (2) is not sufficient.

Combining both statements, considering (II) and (III) from First Cases and (I) and (II) from Second Cases, we can decide (C)

eakabuah · Answer

We are given that p and q are integers such that p^q = 16. We are to determine |p-q|

Since p and q are integers, we only need to find the possible integral values of p^q=16
There are three possibilities: 
2^4, where p=2 and q=4, and |p-q|=|q-p|=2
4^2, where p=4 and q=2, and |p-q|=|q-p|=2
16^1, where p=16 and q=1, and |p-q|=|q-p|=15

Statement 1: q!=1
Sufficient. Since either p=2 and q=4 or p=4 and q=2. In each of this cases, |p-q|=|q-p|=2

Statement 2: p>0
Insufficient since we know p can be 2, 4, or 16 and when p=2 or p=4, |p-q|=2. But when p=16, |p-q|=15.

A is the answer.

freedom128 · Answer

1)
P=4, Q=2, |P - Q| = 2
P=-4, Q=2, |P - Q| = 6
P=2, Q=4, |P - Q| = 2
P=-2, Q=4, |P - Q| = 6
NOT SUFFICIENT

2)
P=4, Q=2, |P - Q| = 2
P=16, Q=1, |P - Q| = 15
P=2, Q=4, |P - Q| = 2
NOT SUFFICIENT

1)+2)
P=4, Q=2, |P - Q| = 2
P=2, Q=4, |P - Q| = 2
SUFFICIENT

FINAL ANSWER IS (C)

Posted from my mobile device

lacktutor · Answer

If P and Q are integers and P^Q = 16, what is the value of |P - Q| ?

( Statement1 ): Q ≠ 1
It could be  2^{4} ,  4^{2} ,  (-2)^{4}  or  (-4)^{2} 
 |2-4|=2, |4-2|=2, |-2-4|=6 or |-4-2|=6  
 Insufficient

( Statement2 ): P > 0
 16^{1}=16  -->  |16-1|=15 
 2^{4}= 16  -->  |2-4|= 2 
 Insufficient

Taken together 1 &2, 
 2^{4}=16 --> |2-4|=2 
 4^{2}= 16 --> |4-2|= 2 
 Sufficient

The answer is C.

sarvesh93sah · Answer

Soln:
P & Q are integers. +ve or -ve.
Possible values for (P,Q) are (-4,2),(-2,4),(2,4),(4,2),(16,1).
Possible values of |P-Q|
|P-Q|=|-4-2|=|-2-4|=6
|P-Q|=|2-4|=|4-2|=2
|P-Q|= |16-1| =15.

Statements:
1) Q not equal to 1.
So, P cannot be 16. But, We don't know whether P is +ve or -ve.
Not sufficient

2) P>0
Shows P is +ve. But P maybe 2,4 or 16. 
Not sufficient

Combining, P is +ve and not 16. So |P-Q|=2
Answer C

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If P and Q are integers and P^Q = 16, what is the value of |P - Q| ?

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