What is m + n ? (1) 2^m*3^n = 648 (2) |m| + |n| = 7

Question

What is  m + n  ?

(1)  2^m*3^n = 648

(2)  |m| + |n| = 7

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imeanup · Answer

1.  2^m∗3^n=648 = 216*3=6^3*3=(3*2)^3*3=3^4*2^3 
Therefore,  m=3; n=4

Sufficient.

2. |m|+|n|=7

m=-4; n=3 =>m+n=-1 ,or, m=4;n=-3 => m+n=1

Insufficient

IMO  Ans A

XSatishX · Answer

Statement 1:  Sufficient 
2^m∗3^n=648. We can easily calculate the values of m and n. 648 = 2^3*3^4 so m=3 and n=4.

Statement 2:  Not Sufficient 
|m|+|n|=7 if m=4 and n=3 than yes m+n=7 but if m=4 and n=-3 than m+n=1.

Correct answer is A

ocelot22 · Answer

(1) 648=2*2*2*3*3*3*3=2^3*3^4 m=3, n=4 sufficient

(2) Let m=3, n=4 |m| +|n| = 3+4 =7 and m=7 as well. Let m=-3 , n=4, |m| +|n| =7, but m+n = 1

Not sufficent. OA is A, 600 level question

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Bunuel · Answer

The question is not that easy.

Deepakjhamb · Answer

Answer is c since it’s not given that m and n are necessarily integers but if we combined both statements only solution possible would be m= 4 and n = 3

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TestPrepUnlimited · Answer

Note nothing was mentioned about m or n so we cannot assume they are integers.

Statement 1:

This would have infinitely many solutions however only one solution is an integer solution as  648 = 8*(75+6) = 8*81 = 2^3*3^4 . Insufficient.

Statement 2:

m and n can be both positive or both negative. Insufficient.

Combined:

If both m and n were positive then we'd have m = 3 and n = 4 as a solution. We may try finding another solution, assume m is negative while n is positive. Then  n - m = 7  and  n = m + 7 . Try plugging that into the first equation to see if it makes sense, we'd have:

2^m *3^{m + 7} = 2^3*3^4 
 6^m=2^3*3^4/3^7=(\frac{2}{3})^3

Since the result is a fraction, we can confirm m is a negative number. Then n is a number less than 7, so there is a possible second solution. For this solution, we already have n - m = 7 so n + m cannot be 7. Thus the value of m+n is not known. Insufficient.

(The 2nd solution is roughly m = -0.68 and n = 6.32, try plugging that in the first equation with a calculator!)

Ans: E

Pankaj0901 · Answer

Deepakjhamb · Answer

Pankaj0901  -0.68 is just a metaphor that has been used but it proves that some negative number and some postive number exist that can give solution

so considering  TestPrepUnlimited  solution i would say answer should be e)\

asking  Bunuel  to confirm

Pankaj0901 · Answer

Deepakjhamb  - Not convincing enough that -0.68 is just a metaphor. Could you please suggest some solutions (assuming there are infinite solutions) which would give the value of expression EXACTLY equal to 648?

Not sure if there's something I am missing.

zhanbo   VeritasKarishma  - Request your views please.

Deepakjhamb · Answer

Pankaj0901  - we just need to understand that it can be an irrational number which definitely u can not write without some approx but it does exist , hope this helps

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Bunuel · Answer

Yes, the OA is E. Edited the OA. Thank you.

What is m + n ? (1) 2^m*3^n = 648 (2) |m| + |n| = 7

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