2 problems

Hi, there. I'm happy to help. I'll do the two questions in two different posts, for clarity.

1) A metal equipment factory produced two batches of screws. The first batch had 2 percent of the screws defective. The second batch was half the size of the first and had 7 percent of defective screws. If the total amount of defective screws produced was 44, how many screws were made in the first batch?
A - 400
B - 800
C - 784
D - 1156
E - 1200

I'm going to say that the second batch has a size of N, so the first batch has a size of 2N.

Number of screws defective in first batch = 0.02*(2N) = 0.04N

Number of screws defective in second batch = 0.07*N = 0.07N

Total number of defective screws = 0.04N + 0.07N = 0.11N = 44

N = 44/0.11 = 4400/11 = 400

There are 400 in the second batch, and twice as many, 800, in the first batch.

Answer = B

Here's another practice question on percents.
https://gmat.magoosh.com/questions/947
When you submit your answer to this question, the following page will have the video explanation.

Does this make sense? Let me know if you have any further questions.

Mike

Hi, there. Now, I'll do the second question.

2)If a travel agency sells t plane tickets in 3 hours, how many hours will it take to fill a plane with s available seats?
A - s/3t
B - 3s/t
C - 3/st
D - 3t/s
E - t/3s

I will show two different methods, a complete solution with each.

Method One: Algebraic

The sell t tickets in 3 hours, so the rate of selling tickets is 3/t. (Of course, as anyone in sales knows, it's entirely unrealistic to assume a constant rate, but we have to do that to solve the problem.)

We know, in general

Amount = (Rate)*(Time)

so here

# of tickets = (Rate of ticket sales)*(Time)

s = (t/3)*(Time)

Time = s/[t/3] = 3s/t

Answer = B

Method Two: Numerical Substitution

Let's pick some unusual numbers, with just enough in common so they are divisible. Let's say t = 21, so they sell 21 in 3 hours, or 7 in a hour. Let's say they have to sell 77 tickets, so that will take 11 hours. (Notice, I am trying to get as many different prime numbers among the numbers I pick as possible.)

For s = 77 and t = 21, we want the time to equal 11.

A - s/3t = 77/(3*21) = 77/63 = not a whole number
B - 3s/t = (3*77)/21 = 77/7 = 11
C - 3/st = 3/(21*77) = whatever that is, it's not a whole number
D - 3t/s = 3*21/77 = 63/77 = not a whole number
E - t/3s = 21/(3*77) = not a whole number

Therefore, answer = B.

Here's a blog article I wrote about the picking-numbers strategy for DS.
https://magoosh.com/gmat/2012/gmat-data- ... ugging-in/

I hope all this is helpful. Please let me know if you have any further questions.

Mike