if a^2 * a^b = a^z ,

Question

GMATBusters’ Quant Quiz Question -4 
if  a^2 * a^b = a^z , What is the value of z?
1) b = 3
2) 2a+2b= 10

GMATBusters · Accepted Answer

if  a^2 * a^b = a^z , What is the value of z?
1) b = 3
2) 2a+2b= 10

Official Solution :  
a^2 * a^b = a^(a+b)
but we know  1^n is always one 
and  0^n is always 0  (except 0^0 which is not defined)
 (-1)^odd integer is always -1 
 (-1)^even integer is always 1

hence,  if a = 1 or 0, z can be any other value also. z need not to be equal to 2+b

Example  1^2*1^3  can be written as  1^9  also, because both = 1

Statement 1:
b = 3, but we do not know whether a = -1, 0, 1 or other number.
NOT SUFFICIENT

Statement 2:
2a+2b= 10
a+b = 5
but we do not know whether a = -1, 0, 1 or other number.
NOT SUFFICIENT

If I combine both statements, a= 2, b = 3
now since a is NOT equal to -,1, 0, 1 . z must be equal to 2+b
z = 5
SUFFICIENT
 Answer C

MayankSingh · Answer

IMO A

Z= (2+b)

From 1) b=3
Z= 5 
Sufficient

From 2) a+b=5
But b not known
Not Sufficient

NikuHBS · Answer

a^(2+b) = a^z
So, b+2 = z or a=1 or 0

Statement 1: 
b= 3 or a=1 or 0
Not Sufficient

Statement 2:
a+b = 5
There are many combinations Not sufficient.

Together,
We get a=2 and b=3 
hence, Z= 3

Option C

ashwini2k6jha · Answer

Answer:A
given a^2 x a^b=a^z
 2+b=z
State 1:sufficient
given b=3
z=3+2=5
State 2:not sufficient
given a+b=5
1st combination a=1 b=4,hence z=6
2nd comb a=2,b=3, z=b+2=5

monikakumar · Answer

if a2∗ab=az, What is the value of z?
1) b = 3
2) 2a+2b= 10

2+b=z

1) z=5
sufficient

2) a+b=5
z=2+b
insufficient

Ans A

dragonking · Answer

Answer is A
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient

nkme2007 · Answer

Given a^2∗a^b=a^z
=>a^(b+2) = a^z
=> z=b+2

Statement 1:  b=3
=> z=5

SUFFICIENT

Statement 2:  2a+2b=10
=>a+b = 5

There can be no fixed value of b as a is variable.
Hence, INSUFFICIENT

OA: A

You owe me a kudos if I am correct, Praveen.

urshi · Answer

Option A

Spunk17 · Answer

IMO a
a^(2+b)=z^z
from the first statement we have b=3 so z can be calculated.
From the second statement we have a+b=5, which does not give us enough information to calculate the answer.

nothing345 · Answer

if a2∗ab=aza2∗ab=az, What is the value of z?
1) b = 3
2) 2a+2b= 10

S1: the powers of (a^2)(a^b)=(a^z) may be simplified to 2+b=z as the base is the same. S1 provides us the value of b which we substitute back in to obtain 2+3=5=z

S2: 2a+2b=10, divide the expression by 2 to get a+b=5. Don't need any further calculations since we defined a+b=z earlier and now we are directly given the value of z.

Therefore, Answer is D.

YuvarajUmapathi · Answer

if a^2∗a^b=a^z, What is the value of z?
1) b = 3
2) 2a+2b= 10

a^(2+b) = a^z
z = 2+b ---------------- 1

From statement 1, b=3

From eqn 1,
z = 5 , sufficient

From statement 2, 2a+2b = 10

a+b = 5 ------- 2
z = 2+ b

we have two equation with three unknown, insufficient

IMO Answer : A

Saasingh · Answer

OA A?

a^2 x a^b = a^ z.

===> a^(2+b ) = a^ z
===> b+2 = z???

(1) b = 3, clearly we can find z as 5. Sufficient.

(2) a+b = 5 , but we dont get a. So we cant find z. Insufficient.

Answer D

Posted from my mobile device

123456789007 · Answer

only option one is sufficient a^2*a^3=a^5

aggvipul · Answer

This is the easiest of all 5 ques.

it follows,  a^(2+b)  =  a^z

1. b=3
z= 5, sufficient

2. a + b = 5
b= 3
z= 5, sufficient

Ans. D

RuchirB · Answer

From properties of exponents we have
2+b =z 
i.e. the value of z is dependent on b.

From statement 1 -> b=3; SUFFICIENT
From statement 2 -> a+b =5; Two unknowns; NOT SUFFICIENT

The answer is A.

Kinshook · Answer

Asked: if  a^2 * a^b = a^z , What is the value of z?
1) b = 3
 a^{2+b} = a^z 
 a^5 = a^z 
If a=0 or 1; z may be any number
If a=-1; z may be any odd number
But if a is any other number; z = 5
NOT SUFFICIENT

2) 2a+2b= 10
a + b = 5
If a=0 or 1; b=5 or 4; z may be any number
If a=-1; z is any odd number
Since b is unknown
NOT SUFFICIENT

(1) + (2) 
1) b = 3
2) 2a+2b= 10
a = 2; b=3
 2^2*2^3 = 2^z 
 2^5 = 2^z 
z = 5
SUFFICIENT

IMO C

if a^2 * a^b = a^z ,

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GMAT Data Sufficiency (DS) Questions

if a^2 * a^b = a^z ,

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