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QUESTION: 231

Which of the lines shown in the xy-plane contains only points with coordinates (x, y) for which x = - y?

Answer(s): B

Explanation:

The equation x = -y represents the line through the origin that slopes downward from left to right (for example, through (-3,3) and (3, -3))
In the diagram, that line is labeled R.

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QUESTION: 232

Which of the following is NOT the sum of a set of consecutive positive integers one of which is 1?

Answer(s): E

Explanation:

A set of consecutive positive integers that includes 1 must be 1, 2, 3, ..., k for some positive integer k.
Its sum is a triangular number:

List triangular numbers up to the largest option:
k = 1 1
k = 2 3
k = 3 6
k = 4 10
k = 5 15
k = 6 21
k = 7 28
k = 8 36
Among the given choices, 3, 10, 15, and 28 appear in this list, but 35 does not.

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QUESTION: 233

An alumnus contributed $50,000 to a university for research. The university deposited the money in a new account at an annual interest rate of 10 percent, compounded annually, for 2 years.

If 60 percent of the interest earned from this account was then withdrawn, what was the total amount left in the account?

$54,000
$54,200
$56,300
$60,000
$60,500

Answer(s): B

Explanation:

The account grows for 2 years at 10% interest compounded annually:
50,000(1.10)2 = 50,000 × 1.21 = 60,500

So, the interest earned is
60,500 - 50,000 = 10,500
If 60% of that interest is withdrawn,
0.60 × 10,500 = 6,300 is withdrawn,
leaving
10,500 - 6,300 = 4,200 of interest in the account.
Thus the balance after the withdrawal is 50,000 + 4,200 = 54,200.

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QUESTION: 234

The table above shows the size of orders placed with a certain shipping company and the number of orders of each size.

Which of the following statements are true? (Choose all that apply.)

There were 5 orders that each included at least 6 items.
There were more orders of size 3 than orders of any other size.
The average (arithmetic mean) size of the orders was 4.25 items.

Answer(s): B

Explanation:

Orders of size 3: 4 orders, which is more than size 2 (1), size 5 (2), or size 7 (3)

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QUESTION: 235

The random variable X has the standard normal distribution with a mean of 0 and a standard deviation of 1, as shown. Probabilities, rounded to the nearest 0.01, are indicated for the six intervals shown. The random variable Y has a normal distribution with a mean of 2 and a standard deviation of 1.

Using the probabilities shown, approximately how much greater is the probability that the value of Y is between 1 and 2 than the probability that the value of X is between 1 and 2?