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OG13 word problems on rates and sets (137 and 178)

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OG13 word problems on rates and sets (137 and 178)

by machadog » Fri Jun 20, 2014 11:49 pm
Hello. This is my first post on the forums, however I have been visiting regularly since I started studying following the 60 day guide.

Today I came across two problems that I wanted to review here.

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I had never come across the need to factor a cuadratic equation of this sort, and I wanted to know if you can suggest alternatives to approaching this problem without having to factor a 24-28 quadratic equation. Very difficult to manage it under 2 minutes!

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I have read the solution explanation several times but cannot seem to grasp the logic behind the explanation. Could someone kindly explain in a different manner or perhaps suggest an alternative way for solving this problem?

Thanks!
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by [email protected] » Sat Jun 21, 2014 1:11 am
Hi machadog,

In the future, it's best to post just one GMAT question per thread (so that the conversation can stay focused on that one item).

The two questions that you listed DON'T actually require you to use a Quadratic; that's just how the book went about explaining those questions.

For question 137, you can actually TEST THE ANSWERS. One of those answers, when "plugged in" to the information in the prompt, WILL match perfectly. You just need to do the necessary arithmetic to find it.

For question 178, you have a much rarer issue. You can either draw a 3-circle Venn Diagram OR you can use the following equation:

Total = Gp1 + Gp2 + Gp3 - (Both1&2) - (Both2&3) - Both(1&3) - 2(All3)

I suggest that you re-attempt these questions with the above approaches. If you get stuck, then post back here and I'll be happy to walk you through the steps.

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by GMATGuruNY » Sat Jun 21, 2014 1:40 am
At his regular hourly rate, Don had estimated the labor cost of a repair job as $336 and he was paid that amount. However, the job took 4 hours longer than he had estimated and, consequently, he earned 2$ per hour less than his regular hourly rate. What was the time Don had estimated for the job, in hours?

28
24
16
14
12
We can PLUG IN THE ANSWERS, which represent the estimated time: 28, 24, 16, 14, or 12.
The actual time was 4 hours longer: 32, 28, 20, 18, or 16.
Both the estimated time and the actual time must divide evenly into 336 (the labor cost).
Since 336 is not a multiple of 32, eliminate A.
Since 336 is not a multiple of 20, eliminate C.
336 is not a multiple of 9, since the sum of its digits is not a multiple of 9.
Thus, 336 is not a multiple of 18; eliminate D.

The correct answer must be B or E.

Answer choice B: estimated time = 24, actual time = 28
Estimated payrate = 336/24 = 14.
Actual payrate = 336/28 = 12.
Difference = 14-12 = 2.
Success!

The correct answer is B.

Note that we had to try only ONE answer choice -- a very efficient way to solve the problem.
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by GMATGuruNY » Sat Jun 21, 2014 1:42 am
Of the 300 subjects who participated in an experiment using virtual-reality therapy to reduce their fear of heights, 40 percent experienced sweaty palms, 30 percent experienced vomiting, and 75 percent experienced dizziness. If all of the subjects experienced at least one of these effects and 35 percent of the subjects experienced exactly two of these effects, how many of the subjects experienced only one of these effects?

A) 105

B) 125

C) 130

D) 180

E) 195
Here is one formula for 3 overlapping groups:

T = A + B + C - (AB + AC + BC) - 2(ABC)

The big idea with overlapping group problems is to SUBTRACT THE OVERLAPS.
When we add together everyone in A, everyone in B, and everyone in C:
Those in exactly 2 of the groups (AB+AC+BC) are counted twice, so they need to be subtracted from the total ONCE.
Those in all 3 groups (ABC) are counted 3 times, so they need to be subtracted from the total TWICE.
By subtracting the overlaps, we ensure that no one is overcounted.

In the problem above:
Let T = 100%.
Sweaty palms = 40.
Vomiting = 30.
Dizziness = 75.
Exactly 2 of the groups = 35.
Let x = the percentage in all 3 groups.

Plugging these values into the formula, we get:
100 = 40 + 30 + 75 - 35 - 2x
100 = 110 - 2x
x=5.

Since 35% are in 2 of the groups and 5% are in all 3 groups, the percentage in exactly one of the groups = 100-35-5 = 60.
Number in exactly one of the groups = .6(300) = 180.

The correct answer is D.
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by Brent@GMATPrepNow » Sat Jun 21, 2014 6:23 am
At his regular hourly rate, Don had estimated the labor cost of a repair job as $336 and he was paid that amount. However, the job took 4 hours longer than he had estimated and, consequently, he earned 2$ per hour less than his regular hourly rate. What was the time Don had ESTIMATED for the job, in hours?

28
24
16
14
12
Here's an algebraic solution:

Let h = # of hours that Don ESTIMATED for the job.
So, h + 4 = ACTUAL # of hours it took Don to complete the job.

So, IF Don, had completed the job in h hours, his RATE would have = $336/h
However, since Don completed the job in h+4 hours, his RATE was actually = $336/(h + 4)

...consequently, he earned 2$ per hour less than his regular hourly rate.
In other words, (John's estimated rate) - 2 = (John's actual rate)
So, $336/h - 2 = $336/(h + 4)

ASIDE: since the above equation is a bit of a pain to solve, you might consider plugging in the answer choices to see which one works.

Okay, let's solve this: $336/h - 2 = $336/(h + 4)
To eliminate the fractions, multiply both sides by (h)(h+4) to get: 336(h+4) - 2(h)(h+4) = 336h
Expand: 336h + 1344 - 2h² - 8h = 336h
Simplify: -2h² - 8h + 1344 = 0
Multiply both sides by -1 to get: 2h² + 8h - 1344 = 0
Divide both sides by 2 to get: h² + 4h - 672 = 0
Factor (yeeesh!) to get: (h - 24)(h + 28) = 0
Solve to get: h = 24 or h = -28
Since h cannot be negative (in the real world), h must equal 24.

Answer: B

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