If m is a positive integer, is the value of p + q at least twice the

Question

If m is a positive integer, is the value of p + q at least twice the value of 3^m + 4^m?

(1) p = 3^(m+1) and q = 2^(2m+1)
(2) m = 4

KarishmaB · Accepted Answer

When I look at the question, I first say to myself, "I definitely need stmnt 1 since I don't know what p and q are." The only point is whether stmnt 2 is required or not since if I have value of m as well, I get the values of all the variables and the answer becomes an easy C. But then, easy C's are generally trickier than they let on. So let me try to see if stmtn 1 alone is sufficient.

p + q  =  3^{m+1} + 2^{2m+1}

In the question stem,  4^m = 2^{2m} 
Question: Is  3^{m+1} + 2^{2m+1}  at least twice of  3^m + 2^{2m}?

or Is  3*3^m + 2*2^{2m}  at least twice of  3^m + 2^{2m}?

Now, if m is a positive integer, can I say
 2*3^m + 2*2^{2m}  is twice of  3^m + 2^{2m}?  Yes!

Then  3*3^m + 2*2^{2m}  is certainly more than twice of  3^m + 2^{2m} , isn't it? 
It is. Hence stmnt 1 is sufficient. Answer (A)

mn2010 · Answer

Is it A ?

Statement 2 is insuff by itself

Statement 1 becomes 
p = 3^m * 3 and q= 4^m * 2
so given m is positive and integer, lowest value of m = 1 which makes p+q = 3*3 + 4 * 2 (lowest value) which is greater than inequality in the prompt ...

Hence A.

amit2k9 · Answer

p+q >= 2 (3^m + 4^m) and m > 0 , integer.

a p+q = 3* 3^m + 2* 4^m

for m= 1, 2,3 LHS p+q = 9+8 = 17 RHS = 7*2 = 14

LHS = 27 + 32 = 59 RHS = 9 + 16 = 25

LHS = 81 + 128 = 209 RHS = 27+ 64 = 91 All the cases LHS > 2 * RHS

Sufficient.

b tells nothing about p+q. Not sufficient.

Hence A.

jamifahad · Answer

If m is a positive integer, is the value of p + q at least twice the value of 3^m + 4^m?
(1) p = 3^(m+1) and q = 2^(2m+1)
(2) m = 4

Given: m>0, 
Is p+q>= 2(3^m+4^m) ?
=>P+q >= 3^m*2 + 4^m * 2

Stmt:1 p=3^(m+1)=>3^m*3
 q=4^m+2
p+q=3^m*3+4^m+2. 
p+q=3^m*(2+1) + 4^m+2
p+q=3^m*2 + 3^m + 4^m+2
p+q=  + 3^m 
Hence p+q is definitely greater than 3^m*2+4^m*2
Sufficient.

Stmt2: m=4. p+q>=3^4*2+4^4*2
Doesn't say anything about p and q. Insufficient.

OA A.

Bunuel · Answer

This is a copy of an OG question: if-n-is-a-positive-integer-is-the-value-of-b-a-at-least-144344.html

mejia401 · Answer

Since common bases with one variable can be solved, providing the values for p and q under the same common bases allows for the solution, and therefore is sufficient. A

yezz · Answer

from 1

is

3^(m+1) + 2^(2m+1) >= 2(3^m +4^m) , i.e. is 3(m+1) + 2^(2m+1) >= 2*3^m + 2^(2m+1)

is 3^(m+1) >= 2* 3^m , is 3 >=2 sure ... suff
from 2 clearly insuff

A

bumpbot · Answer

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If m is a positive integer, is the value of p + q at least twice the

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If m is a positive integer, is the value of p + q at least twice the

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