If a certain wheel turns at a constant rate of x revolutions per minut

Question

If a certain wheel turns at a constant rate of x revolutions per minute, how many revolutions will the wheel make in k seconds?

(A)  60kx

(B)  kx

(C)  \frac{x}{k}

(D)  \frac{x}{60k}

(E)  \frac{kx}{60}

EMPOWERgmatRichC · Answer

Hi All,

This question can be solved algebraically or by TESTing VALUES.

We're told that a wheel turns at a constant rate of X revolutions per MINUTE. We're asked for the number of revolutions the wheel makes in K SECONDS.

IF....
X = 10 revolutions per minute = 10 revolutions per 60 seconds = 1 revolution per 6 seconds
K = 6 seconds
The wheel will turn 1 revolution in 6 seconds.

So we're looking for an answer that equals 1 when X = 10 and K = 6. There's only one answer that matches...

Final Answer:  E

GMAT assassins aren't born, they're made,
Rich

ScottTargetTestPrep · Answer

Since k seconds is k/60 minutes, the wheel will make x * k/60 = xk/60 revolutions in k seconds.

Answer: E

BrentGMATPrepNow · Answer

We can solve the question using  equivalent ratios

Wheel turns at a constant rate of x revolutions per minute  
We can also say the wheel turns at a constant rate of  x  revolutions per  60  seconds
In other words,  # of revolutions / seconds elapsed  =  x / 60

How many revolutions will the wheel make in k seconds?  
Let  R  = the number of revolutions will the wheel make in  k  seconds
We can now write:  x / 60  =  R / k 
To solve for R, we can first cross multiply to get: 60R = kx
Divide both sides by 60 to get: kx/60

Answer: E

RELATED VIDEO
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gmatchile1 · Answer

Yes the answer is (E), but why?
Hello, my name is Claudio Hurtado, GMAT FOCUS EDITION coach for the Quantitative Reasoning (mathematics) and Data Insight sections (graphs, tables, interpretation and data sufficiency, the latter in the old GMAT was part of the quantitative section). I will gladly help you visualize the correct approach to this problem solving, to understand why the answer is (E).

Namely, 1 minute is associated with 60 seconds, we can write this as a ratio, that is:

1m/60sec, so we can build the relationship between 1 second and minutes, that is, we can answer the question: How many minutes does 1 second correspond to?

To answer, we need that where seconds appear it takes the value one, in the denominator of 1m/60sec second appears, to make it 1, we must divide numerator and denominator by 60, that is:

(1m/60)/(60sec/60) = (1m/60)/(1sec), so 1 second is equivalent to (1/60)m

If we wanted to know how many minutes 20 seconds are equivalent to, we work like this:
(1/60)m is related to 1sec, then 20x1 sec will be related to 20x(1/60)m, that is, 20 sec will be related to ((20x1)/60)m, then (20/60)m, finally (1/3)m, the third part of 1 minute.

ie) 20 seconds is equivalent to (1/3)m

Now let's go to the situation that calls us:

We must find the relationship between 1m and k seconds, that is, in minutes how many k seconds are, to transform from seconds to minutes, we must divide the seconds by 60, as shown before.

So k seconds are equivalent to (k/60)m.

The statement says that the wheel rotates constantly at a rate of x revolutions per minute, that is, for every minute the wheel makes one revolution.

So in ksec ((k/60)m) the wheel will give X * (k/60) revolutions expressed in another way is kx/60 = kx:60

Alternative (E).

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If a certain wheel turns at a constant rate of x revolutions per minut

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If a certain wheel turns at a constant rate of x revolutions per minut

Prep Toolkit

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

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745 with Only Self-Prep and GMAT Club

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