What is the value of x? (1) x^4 = 2,401 (2) x^5 = 16,807

sudarshan22

GMAT doesn't test negative root, does it?
\(x^2\)=+-x but \(\sqrt{4}\)=2 and never -2


so fourth root of 2401 will always be positive

Am I missing something?

x^4=2401 is different from √x=2401...
Say x^4=16..
X^2=+-4...
X^2 cannot be -4, so x^2=4
Which means X=+-2..

Also if x=-7, x^2=49 and x^4=49*49....
Nothing wrong in this
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Hi dave13,
Nice question indeed!!?
How did I choose \(7^5\)?
GMAT maintains a pattern,i.e, 99% of the times,the test makers set DS questions(value questions with correct option D, such as what is the value of x? ) in such a way that each statement yields the same unique value.

After we are done with st1(we found x to be 7 or -7), on the first sight, our priority is to check statement 2 whether it yields x=7 as a possible value.
Already we have calculated till \(7^4\), hope it is not a cumbersome task to multiply 7 again with \(7^4\).( A quick note in mind:- unit digit of \(7^4\) and 7,when multiplied yield 7 (☺️16807 has units digit 7)).

Hope my thought process helps .

P.S.- An example for you.
Q. What is the value of (a-b)?
1) \((a-b)^4=16\)
2) \((a-b)^5=-32\)

Again ,how did I know 2401=\(7^4\)? Let me answer you before you ask me really. Please apply divisibility rule of 2,3,4,5,6,7 as quickly as possible. I hope you know the divisibility tests.

Another method:- ( without doing anything)
1. You know GMAT lives in real world . So any root(even root or odd root) will always yield a real value.
2.Even roots yield both positive values and negative values when the number is positive. For negative numbers,even root is imaginary. (Here the number is positive,so,from st1 we have two values of x.hence,insufficient)
3. Odd roots yield positive values when the number is positive.Odd roots yield negative values when the number is negative. (Here the number is positive ,so the odd root will yield a positive unique value.Hence sufficient)

If you know the concepts and reasoning, it will hardly take 10s to conclude the answers , subsequently saves 1 minute of your precious time in real exam.
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Yes, you are correct
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(1) x^4 = 2,401
Could be negative square or a positive square
Insufficient

(2) x^5 = 16,807
One value, negative is not possible
Sufficient

Hence, B.
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You're right, that sounds legit, I missed on that in jiffy
Thanks for rectifying the blunder
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(1) \(x^4\)= 2401= \((7)^4\). It could be +or-7\([Insuff]\)

(2) \(x^5\)= 16,807= \((7)^5\). It is always +7 [Suff]

Answer: B.

Does GMAT tests negative root?

chetan2u Sir
Can you please help us clarify the aforementioned doubt ?
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OK..It means in the question under discussion ..For Statement 1) x= +7 & -7 . Since we do not have a unique value of x, Statement 1 is insufficient
This means answer choice B correct ?

Question stem:- x=?

St1:- \(x^4 = 2,401\)
Here we have 4 values of x, viz, 7, -7, 7i, and -7i.
Note:- GMAT accepts only real solutions/values. So, discard 7i and -7i.
Hence, x=7,-7
No unique value of x.
Insufficient.

St2:- \(x^5 = 16,807\)
Or, \(x= 16807^{\frac{1}{5}}\)
Or, \(x= (7^5)^{\frac{1}{5}}\)
Or, x=7 (\(\sqrt[n]{a^n}=a\))
Unique value of x.
Hence, sufficient.

Ans. (B)
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PKN
how did you calculate \((7^5)\) in second statement?
Thanks

Dear chetan2u, thanks again for the clarification. So if I understand correctly, you said that (i) could be both - or + so answer is B. Thanks.


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