If p:q=r:s and r:s=t:v , find the value of ((p^2∗k^z+r^2∗k^z+t

Question

If p:q=r:s and r:s=t:v , find the value of ((p^2∗k^z+r^2∗k^z+t^2∗k^z)/(q^2+s^2+v^2))^1/z

A. k
B. (p/s)^1/z∗k^2
C. (r/v)^z/2∗k 
D. (r/s)^2/z∗k
E. (t/s)^2/z∗k

chetan2u · Accepted Answer

Here is the solution..

( \frac{(p^2∗k^z+r^2∗k^z+t^2∗k^z)}{(q^2+s^2+v^2)} )^{1/z} 
Multiply both denominator and numerator by r^2..

( \frac{r^2(p^2∗k^z+r^2∗k^z+t^2∗k^z)}{(r^2q^2+r^2s^2+r^2v^2)} )^{1/z} ...
Now, p:q=r:s means ps=rq and similarly r:s=t:v means RV=at...
 ( \frac{r^2(p^2∗k^z+r^2∗k^z+t^2∗k^z)}{(p^2s^2+r^2s^2+s^2t^2)} )^{1/z} 
Take out common terms s^2 in denominator and k^z in numerator..
 ( \frac{r^2k^z(p^2+r^2+t^2)}{s^2(p^2+r^2+t^2)} )^{1/z} 
 (\frac{r}{s})^{2/z}*k^{z/z}

D

Fdambro294 · Answer

If unable to see the Algebraic solution, you can substitute easy numbers and match the expression up with the answer choices

P/Q = R/S = T/V

Let
P = 1 and Q = 2

R = 3 and S = 6

T = 4 and V = 8

(1st) there is a common (k)^z in the numerator, so you can take the common factor

(K)^z * ( p^2 + r^2 + t^2)
________________________
(q^2 + s^2 + v^2)

This is all raised to the power of: ^(1/z)
Or
The “Z-Root” is taken on the expression

2nd: Exponent Rule: Power of a Product Rule

(K)^Z power ——-> taking the Z root will make this expression K

And then (1/Z) power is taken on the remaining fraction —- substituting numbers

K *  ^(1/z)
_________________________
 ^(1/z)

K * (26 / 104)^(1/z)

K * (1/4)^(1/z)

K * (1^2 / 2^2) ^(1/z)

Using the nested exponent rule backwards —- the numerator of the fractional exponent is the power the Base is taken to

K * (1/2) ^ (2/z)

The base of 1/2 is equal to any of the given ratio, so we just need to find an answer that fits

D: since (r/s) = (1/2)

k * (r/s)^ (2/z)

D is the correct answer (can be accomplished in around 2 minutes with accurate and effective arithmetic)

Posted from my mobile device

neha283 · Answer

Can someone post a detailed solution for this? I am not sure how to approach such questions. 
TIA

shubhim20 · Answer

how do we know we have to multiply by r2 in second step

Susmita#4160 · Answer

Taking p + r + t / q + s + v = m and p/q = r/s = t/v also = m as all are of same ratio
p^2 + r^2 + t^2 / q^2 + s^2 + v^2 = m^2

from Q ->   ^1/z = k * m^2/z

Looking at options D matches where we can put m = r/s

If p:q=r:s and r:s=t:v , find the value of ((p^2∗k^z+r^2∗k^z+t

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GMAT Problem Solving (PS) Questions

If p:q=r:s and r:s=t:v , find the value of ((p^2∗k^z+r^2∗k^z+t

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards