Algebra - Inequalities & Statistics - OG(2nd Edition)

shanice wrote:Hi all,

1)List S consists of 10 consecutive odd integers, and List T consists of 5 consecutive even
integers. If the least integer in S is 7 more than the least integer in T, how much greater is the
average(arithmetic mean) of the integers in S than the average of the integers in T?

A)2 B)7 C)8 D)12 E)22

When the values in a set are evenly spaced, the mean = the median.

Let the least integer in T = 2.
Thus, T = {2,4,6,8,10}.
Mean = median = 6.

Since the least integer in S is 7 more than the least integer in T, the least integer in S = 2+7 = 9.
Thus, S = {9,11,13,15,17,19,21,23,25,27}.
Mean = median = (17+19)/2 = 18.

Mean of S - mean of T = 18-6 = 12.

The correct answer is D.

shanice wrote:Hi all,

1)List S consists of 10 consecutive odd integers, and List T consists of 5 consecutive even
integers. If the least integer in S is 7 more than the least integer in T, how much greater is the
average(arithmetic mean) of the integers in S than the average of the integers in T?

A)2 B)7 C)8 D)12 E)22

Answer is D.


My workings:-

S={1,3,5,7,9,11,13,15,17,19}

Mean = 100/10 = 10

T={2,4,6,8,10}

Mean = 30/5 = 6

Am I correct so far with the above? I don't understand how do I apply this sentence"If the least integer in S is 7 more than the least integer in T"?


2)If b<2 and 2x-3b=0, which of the following must be true?

A)x > 3
b)x < 2
c)x=3
d)x < 3
e)x > 3

Answer is D.

I did plug in numbers but it's not working. I may be wrong.

Please help me with the above two questions.

Thank you.

Hi, Shanice,

For question #1:

What are the topics being tested in question #1?
1. Statistics (to compute for the average)
2. Consecutive multiples (properties of consecutive multiples)

As such:

The condition is that: Least integer in S = 7 + Least integers in T

Start first with T
T {2,4,6,8,10}
Then since you know that the least integer in S = 7 + least integer in T, we have
S {9,11,13,15,17,19,21,23,25,27} - check that 9 - 2 = 7, which satisfies the condition

And then:

We go back to the properties of consecutive multiples. One of the properties states that for any consecutive multiples, the average (mean) is equal to the smallest + biggest divide by 2.

In mathematical terms: average = (smallest + biggest)/2

Check that this process would greatly cut the time you solve the problem instead of adding 9 + 11 + 13 + 15 + 17 (remember you only have 2:00 minutes average per problem)

As such:
Mean of S = (9+27)/2 = 36/2 = 18
Mean of T = (2+10)/2 = 12/2 = 6

Determine: "How much greater is the average of the integers in S than the average of the integers in T?"

Mathematically this is Mean of S - Mean of T = ?

18 - 6 = 12

Hope that helped,
Dave

2x = 3b implies b = 2x/3

Hence, 2x/3 < 2 implies x < 3

Hi Mr.Anurag,

Can you please explain how 2x-3b=0 becomes as above? I still don't understand.

Sorry.