### 11 - 760+: Explanations to the Prior 3 Problem Solving Questions

1) A motorist averaged 40 miles per hour on his way to work. He averaged 70 miles per hour on his way home along the same route. Which of the following is the closest to his average speed for the round trip?

A. 40

B. 51

C. 55

D. 59

E. 59.5

The answers to this question are 'spaced out' in such a way that you don't need to do much math at all to get to the correct answer. This prompt is a fairly common 'design' for a Weighted Average question. Here, a motorist travels a certain distance at one speed, then travels back - the SAME distance - at a different speed. We're asked for the AVERAGE SPEED for the entire trip.

One of the key elements to these types of questions is that the answer will be closer to the slower speed than to the faster speed. The exact 'middle' between 40 and 70 is 55, BUT since the motorist spends MORE time driving 40 mph, the average would have to be closer to 40 (while not being 40 exactly). There's only one answer that 'fits'...

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2) Franny can type 80 words per minute and Matt can type 60 words per minute. If the two together must type up a 14,000-word paper and each person can type for at most 2 hours, what is the least amount of time, in hours, that Matt must type?

A. 2

B. 5/6

C. 11/12

D. 11/9

E. 35/9

The answer choices to this question provide a really nice 'shortcut' that can help you to cut down on the amount of math that is necessary to answer this question. To start, we're told that Franny and Matt can each type UP TO 2 hours, but we're asked for the LEAST amount of time (in hours) that Matt would need to type. Thus, the answer is almost certainly going to be LESS than 2. Eliminate Answer A and Answer E (this answer is almost 4 hours, which is simply not an option based on the information in the prompt).

Given Franny's rate (80 words/minute), we know that in 2 hours she would type (2)(60)(80) = 9600 words. This leaves 14,000 - 9,600 = 4,400 words for Matt.

Given Mat's rate (60 words/minute), the 4400 words would take 4400/60 = OVER 60 minutes. You don't need to calculate the exact value - it's enough to note that Matt would need to spend MORE than 1 hour typing. Answers B and C are LESS than 1 hour, so there's only one answer that makes sense...

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3) At a company meeting, M men and W women meet in a conference room. If there are twice as many men as women at the meeting and the conference room can hold no more than 50 total people, then what is the maximum number of women who can be at that meeting?

A) 15

B) 16

C) 17

D) 18

E) 19

This question can be approached Algebraically or by TESTing THE ANSWERS. Here is how you can get to the solution by TESTing THE ANSWERS.

We're given a couple of facts to work with:

1) There are TWICE as men as women in a conference room

2) The conference room can hold UP TO 50 people.

We're asked for the MAXIMUM number of WOMEN that the room can hold.

Let's TEST Answer D: 18 women

IF... there were 18 women, then there would be 2(18) = 36 men.

18 + 36 = 54, but that is TOO MANY people (the room can only hold up to 50), so this answer is TOO BIG.

Eliminate D and E (that answer would be even BIGGER).

Answer C: 17 women

IF... there were 17 women, then there would be 2(17) = 34 men.

17 + 34 = 51, but that is TOO MANY people (although it's REALLY close), so this answer is TOO BIG.

Eliminate C.

Answer B: 16 women

IF... there were 16 women, then there would be 2(16) = 32 men.

16 + 32 = 48. This is the LARGEST answer that 'fits' all of the information that we've been given, so this MUST be the answer.

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As you continue to study, remember to use EVERY piece of information that each prompt gives you. This idea is relevant in BOTH the Quant and Verbal sections - and is 'key' to maximizing your performance on Test Day.

GMAT assassins aren’t born, they’re made,

Rich

If you have any questions about anything in this thread, then you can feel free to contact me directly via email (at [email protected])