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"Problem Solving" Questions require you to solve the problem, and choose the best answer from the choices given. All numbers are real numbers.

For Quantitative Comparison problems, Choose the appopriate answer describing your decision about which value is greater in the two columns specified, if such a decision can be made. If not, pick the last option.

Q1. QUANTITATIVE COMPARISON

"In a certain group of people, the average(arithmetic mean) I.Q. of the males is 128 and that of the females is 136. The group contains twice as many females as males.

COLUMN A	COLUMN B
The average I.Q. of all members of the group.	133

Value in Column A is greater than that in Column B.
Value in Column B is greater than than in Column A.
Values in Column A and in Column B are equal.
Comparison cannot be made on the basis of information provided.

Q2.PROBLEM SOLVING.

"If X_N = 5_x10^-(N+1), for what value of N is X_N equal to 0.0000000005?"

7
8
9
10⁹
10¹⁰

Q3. PROBLEM SOLVING

"In a sequence, the first three values are the first three prime integers in ascending order, and each of the succeeding values is the sum of all the preceding values, what is the ratio of the Thirtieth value to the Twenty-fifth value in the sequence?"

6/5
32
64
128
2³⁰

Q4. QUANTITATIVE COMPARISON

"In a certain school, 40 more than 1/3^rd of all the students are taking a science course, and , of these, 1/4^th are taking physics. The number of students taking physics is exactly 1/8^th of all the students.

COLUMN A	COLUMN B
Number of students in the school	240

Q5. QUANTITATIVE COMPARISON

-10 < k < 10,
k² > 4
1 - k > 0

COLUMN A	COLUMN B
k	0

Q6.PROBLEM SOLVING.

"If F(X) = {1/X} - {1/(X+1)}, what is the sum of F(1) through F(200), inclusive?"

0
1
100
200/201
1/40200

Q7.PROBLEM SOLVING.

"Seven identical circles - each of radius 1 inch - are arranged tangentially to one another as shown above. What is the area enclosed by the hexagon connecting the centers of the outer circles?"

3
6
6_\/2
6_\/3
Cannot be determined

Q8. QUANTITATIVE COMPARISON

"A ladder of length 10 feet is propped up against a vertical wall such that the bottom of the ladder makes an angle of 60 degrees to the ground. The ladder slips down and the bottom of the ladder moves away from the wall. In this position, the bottom of the ladder makes an angle of 45 degrees to the ground."

COLUMN A	COLUMN B
The distance the ladder slipped along the ground	2

Q9. QUANTITATIVE COMPARISON

"Town T has 20,000 residents, 60 percent of whom are females.
The number of female residents who were born in Town T is twice the number of male residents who were not born in Town T.
The number of female residents who were not born in Town T is twice the number of female residents who were born in Town T.

COLUMN A	COLUMN B
PERCENT OF RESIDENTS BORN IN TOWN T	PERCENT OF RESIDENTS NOT BORN IN TOWN T

Q10. PROBLEM SOLVING

"A hiker walked for two days. On the second day, the hiker walked 2 hours longer and at an average speed 1 mile per hour faster than he did on day 1. If during the two days, he walked a total of 64 miles and spent a total of 18 hours walking, what was the average speed on the first day?"

2 MPH
3 MPH
4 MPH
5 MPH
6 MPH

Q11. PROBLEM SOLVING

"How much greater is the sum of all the even integers than is the sum of all the odd integers in the range between 1 and 200, inclusive?"

0
20
50
80
100

Q12. PROBLEM SOLVING

"Of all the 5 digit integers formed by permutation of the digits 1, 2, 3, 4, and 5 without repetition (for example, 12345 is a valid integer but 11111 is not), what is the probability that a 5 digit integer drawn randomly will be divisible by 4?"

1/5
2/5
3/5
4/5
1/120

Q13. PROBLEM SOLVING

"Chairman Chris, and 4 directors - Paul, Quincy, Roger, and Sam - are to be seated in a row for a photo session.How many different ways can these 5 persons be seated subject to the restriction that Chris and Quincy cannot be seated next to each other in any order?"

24
36
48
64
72

Q14. QUANTITATIVE COMPARISON

"|-5| = -P"

COLUMN A	COLUMN B
-P	P

Q15. PROBLEM SOLVING

"From the even integers in the range between 1 and 9, two different even integers are to be chosen randomly at a time. What is the probability that the sum of integers so selected will be 10?"

1/9
1/6
1/4
1/3
1/2

Q16. PROBLEM SOLVING

"A 3-member rowing team is to be selected from 4 men and 5 women. How many different 3-member teams be formed subject to the requirement that each team have at least 1 woman in it?"

20
80
100
400
528

Q17. QUANTITATIVE COMPARISON

	s
u	t	8
	4

A computer generates non-zero numbers for the figure above such that the product of the numbers along the vertical column is equal to the product of the numbers in the horizontal row. The value of t is 2.

COLUMN A	COLUMN B
Value of s	Value of u

Q18. QUANTITATIVE COMPARISON

"If P, Q, R, S, and T are values on a number line such that

P < Q < R < S < T,

Q = --S

COLUMN A	COLUMN B
value of R	0

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