#49) How many integers n are there such that r < n < s?

You should NEVER assume that all numbers on the GMAT are Integers, until specified. Repeat this mantra a couple of times and look for the solution below.

1) s - r = 5

Case 1: r is an integer. If r is an integer, s = r+5 is also an integer
Let the value of r be 5, then the value of S is 10 and there are 4 integers between r and s(6,7,8,9)
Case 2: r is not an integer.
Let the value of r be 5.1, then the value of S is 10.1 and there are 5 integers between r and s(6,7,8,9,10)

So, we have two answers to the question, hence statement I is insufficient to answer the question.

2) r and s are not integers.

Irrelevant statement

From I and II

Since r and s are not integers, the answer to the question is 5. Hence C

38) Machine X runs at a constant rate and produces a lot consisting of 100 cans in 2 hours. How much less time would it take to produce the lot of cans if both Machines X and Y were run simultaneously?

1) Both Machines X and Y produce the same number of cans per hour.

i.e. Machine Y can produce 100 cans in 2 hours. So, Machine Y can produce 50 cans in 1 hour. Similarly can produce 50 cans in 1 hour. If Machines X and Y were run simultaneously they can produce 50+50 = 100 cans in an hour, saving an hour per lot.

Statement I is sufficient to answer the question.

2) It takes Machine X twice as long to produce the lot of cans as it takes Machines X and Y running simultaneously to produce the lot.

The statement is wordy but says the same as statement I. Let us see how. Machine X takes 2 hours to produce 100 cans. Statement II says that if Machines X and Y were run simultaneously they can produce 100 cans in half of the time taken by Machine X, i.e 1 hour, saving an hour per lot.

Statement II is sufficient to answer the question.

Hence D

S1. Speed X = Speed Y. Speed X is known
Sufficient

S2. Speed X = (Speed X+Y)/2
Sufficient

(D)


Question 2

s-r = 5
If s and r not integers the number of integers = 5
If s and r are integers number of integers = 4

therefore (B) is answer