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help me understand this PS problem

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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help me understand this PS problem

by roc101 » Sat May 24, 2014 12:54 pm
[m] = 3m for all odd m; [m] = 1/2m for all even m. solve [9] X [6]?

I got 81 but the the correct answer is 27 and i can not seem to wrap my head around this seemingly simple problem. Someone please shed some light on what I am doing incorrectly.

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by Brent@GMATPrepNow » Sat May 24, 2014 1:08 pm
roc101 wrote:[m] = 3m for all odd m; [m] = 1/2m for all even m. solve [9] X [6]?

A) (81)
B) (54)
C) (36)
D) (27)
E) (18)
You are correct in that [9] x [6] = 81

9 is odd, so [9] = (3)(9) = 27
6 is even, so [6] = 6/2 = 3
So, [9] x [6] = 27 x 3 = 81

However, the answer choices are as follows:

a) [81]
b) [54]
c) [37]
d) [27]
e) [18]

So, which of these equals 81?

Since 27 is odd, [27] = (3)(27) = 81

So, the correct answer is D

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by [email protected] » Sat May 24, 2014 5:31 pm
Hi roc101,

Brent has correctly explained the math behind this question, so I won't rehash that material here.

This is an example of a "symbolism" question, in which the prompt "makes up" a math symbol, tells you what it means, and asks you to perform a basic calculation with it. You'll likely see 1 of these on the Official GMAT and you appeared to handle the bulk of the work just fine.

You ARE expected to use the symbol wherever it appears, so realizing the symbol appears in the answer choices means that you had a bit more work to do. This "twist" on a symbolism question isn't too common, but as you do better and better in the Quant section, the GMAT will adapt to you and give you more questions that require slightly more work (or that have "twists"). Be on the lookout for those details as you continue to study.

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by roc101 » Sun May 25, 2014 9:46 am
Thank you all!
Could you explain a shortcut to solving this problem below? I definitely went over 2 minutes.
The temperature of a certain cup of coffee 10 minutes after it was poured was 120 degrees F. If the temperature F of the coffee t minutes after it was poured can be determined by the formula F=120(2^-at) + 60, where F is in degrees F and a is a constant, then the temperature of the coffee 30 minutes after it was poured was how many degrees?
65
75
80
85
90

thanks!
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by Brent@GMATPrepNow » Sun May 25, 2014 9:53 am
The temperature of a certain cup of coffee 10 minutes after it was poured was 120 degrees Fahrenheit. if the temperature f of the coffee t minutes after it was poured can be determined by the formula f = 120 * 2^(-at) + 60, where f is in degrees Fahrenheit and a is a constant, then the temperature of the coffee 30 minutes after it was poured was how many degrees Fahrenheit?
A. 65
B. 75
C. 80
D. 85
E. 90
The temperature of a certain cup of coffee 10 minutes after it was poured was 120 degrees Fahrenheit.

So, 120 = 120 * 2^[(-a)(10)] + 60
Divide both sides by 60: 2 = 2 * 2^[(-a)(10)] + 1
1 = 2 * 2^[(-a)(10)]
1/2 = 2^[(-a)(10)]
Since 2^(-1) = 1/2, we know that (-a)(10) = -1
So, a = 1/10

So, the formula is f = 120 * 2^[(-1/10)(t)] + 60

The temperature of the coffee 30 minutes after it was poured was how many degrees Fahrenheit?
f = 120 * 2^[(-1/10)(30)] + 60
= 120 * 2^[-3] + 60
= 120 * (1/8) + 60
= 15 + 60
= 75
= B

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Brent
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by roc101 » Sun May 25, 2014 10:16 am
any guidance on this?
Two water pumps, working simultaneously at their respective constant rates, took exactly 4 hours to fill a certain swimming pool. If the constant rate of one pump was 1.5 the constant rate of the other, how many hours would it have taken the faster pump to fill the pool if it had worked alone at its constant rate?
5
16/3
11/2
6
20/3
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by [email protected] » Sun May 25, 2014 10:34 am
Hi roc101,

For future questions, you should plan to post each individually (in its own thread). You'll likely receive more responses and perspective from the experts and users in this Forum.

This is an example of a Work Formula question. Any time you have two entities (people, machines, water pumps, etc.) working on a job together, you can use the following formula:

(AB)/(A+B) = Total time to do the job together

Here, we're told that the total time = 4 hours and that one machine's rate is 1.5 times the other machine's rate...

If B = 1.5A then we have...

(A)(1.5A)/(A + 1.5A) = 4

1.5A^2/2.5A = 4

1.5A^2 = 10A

A^2 = 20A/3

A = 20/3 hours to fill the pool alone

With this info, we can plug back in and figure out the rate of the other pump (B = 10, so it would take 10 hours to fill the pool alone)

Final Answer: E

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