means that n is the square of a prime number. Of
the integers between 1 and 16 , inclusive, only 4
and 9 are the squares of prime numbers.The correct answer is B.
PS06288- If d = 2 .0453 and d is the decimal obtained by
rounding d to the nearest hundredth, what is the value
of d - d?
(A) -0.0053
(B) -0.0003
(C) 0.0007
(D) 0.0047
(E) 0.0153Arithmetic
Since d = 2.0453 rounded to the nearest
hundredth is 2.05, d* = 2.05; therefore,
d*—d= 2.05 -2.0453 = 0.004 7.1h e correct answeris D.
PS14063 1- Stephanie has 2 —cups of milk on hand and makes
(^4 2)
2 batches of cookies, using -cup of milk for each
3
batch of cookies. Which of the following describes the
amount of milk remaining after she makes the cookies?
(Al
(B)
(C)
(D)
(E)
Less than^1 -
2
cup
Between^1 —^3
2
cup and -
4
cup
Between -
4
(^3) cup and 1 cup
1
Between 1 cup and 1-
2
cups
1
More than 1 —
2
cups
Arithmetic
In cups, the amount of milk remaining is
2 1- (^2) (勹=2._.1=^27 -1^6 卫，whichis
4 3 4 3 12 12
greater than -^3 =—^9 and less than 1.
4 12
1h e correct answer 1s C.
4.5 Answer Explanations
PS01656
- The expression n! is defined as the product of the
integers from 1 through n. If p is the product of the
integers from 100 through 299 and q is the product
of the integers from 200 through 2 99, which of the
following is equal to—?p
q
(Al 99!
(8) 199!
(C)199!
99!(D)^2 99!
99!(E) 299!
199!
Arithmetic
The number pis equal to 100 x 101 x 102 x
...x 299 and the number q is equal to
200 X 201 X 202 X...x 299. The number 1_
q
is thus equal to^100 xlOl x 102x ... x^299 ＝
200 X 201 X 202 X ... X 299
100 x 101 x 102x ... x 199 x 200 x 201 x 202x ... x 299
200 X 201 X 202X ... X 299
Canceling 200 x 201 x 202 x ... x 299 from the
numerator and the denominator, we see that- p = 100 xlOl x102x...x 199. Note that the
q
multiplication in this expression for - begins p
q
with 100 (the smallest of the numbers being
multiplied), whereas the multiplication in
n! = 1 X 2 X 3 X...x n begins with 1. Starting
with 199! as our numerator, we thus need to find
a denominator that will cancel the undesired
elements of the multiplication (in 199!).
This number is 1 x 2 x 3 x ... x 99 = 99!
That is, —= 100 p xlOl x 102 x ... x 199 =
q
1 x 2 x 3 x ... x 99x100 xlOl x 102 x ... x 199 ＝ 199!
lx2x 3x ... x99 99!
1h e correct answer 1s C.