[Math Center]

1. A certain store sells two types of pens: one type for $[latex]2[latex] per pen and the other type for $[latex]3[latex] per pen. If a customer can spend up to $[latex]25[latex] to buy pens at the store and there is no sales tax, what is the greatest number of pens the customer can buy?

(A) [latex]9[latex]
(B) [latex]10[latex]
(C) [latex]11[latex]
(D) [latex]12[latex]
(E) [latex]20[latex]


2. A certain shipping service charges an insurance fee of $[latex]0.75[latex] when shipping any package with contents worth $[latex]25.00[latex] or less and an insurance fee of $[latex]1.00[latex] when shipping any package with contents worth over $[latex]25.00[latex]. If Dan uses the shipping company to ship three packages with contents worth $[latex]18.25[latex], $[latex]25.00[latex], and $[latex]127.50[latex], respectively, what is the total insurance fee that the company charges Dan to ship the three packages? 

(A) [latex]1.75[latex]
(B) [latex]2.25[latex]
(C) [latex]2.50[latex]
(D) [latex]2.75[latex]
(E) [latex]3.00[latex]


3.  At a fruit stand, apples can be purchased for $[latex]0.15[latex] each and pears for $[latex]0.20[latex] each. At these rates, a bag of apples and pears was purchased for $[latex]3.80[latex]. If the bag contained [latex]21[latex] pieces of fruit, how many of the pieces were pears?


4. A theater sells children’s tickets for half the adult ticket price. If [latex]5[latex] adult tickets and [latex]8[latex] children’s tickets cost a total of $[latex]27[latex], what is the cost of an adult ticket?


5.  A group can charter a particular aircraft at a fixed total cost. If [latex]36[latex] people charter the aircraft rather than 40 people, then the cost per person is greater by $[latex]12[latex].

(a) What is the fixed total cost to charter the aircraft?
(b) What is the cost per person if [latex]40[latex] people charter the aircraft?


6. [latex]1[latex] Pound = [latex]16[latex] Ounces

Quantity A Quantity B
Weight of [latex]16,000[latex] ounces of rice Weight of [latex]1,000[latex] pounds of coal



Quantity A Quantity B
Distance between point [latex]A[latex] and a point that is located [latex]8[latex] miles East of point [latex]P[latex], if Point [latex]P[latex] is located [latex]6[latex] miles North of point [latex]A[latex] Distance between point [latex]B[latex] and a point that is located [latex]6[latex] miles West of point [latex]Q[latex], if Point [latex]Q[latex] is located [latex]8[latex] miles South of point [latex]B[latex]


8. A project has three test cases. Three teams are formed to study the three different test cases. James is assigned to all three teams. Except for James, each researcher is assigned to exactly one team. If each team has exactly [latex]6[latex] members, then what is the exact number of researchers required?

(A) [latex]10[latex]
(B) [latex]12[latex]
(C) [latex]14[latex]
(D) [latex]15[latex]
(E) [latex]16[latex]


9.  John has $[latex]42[latex]. He purchased fifty mangoes and thirty oranges with the whole amount. He then chose to return six mangoes for nine oranges as both quantities are equally priced. What is the price of each Mango?

(A) [latex]0.4[latex]
(B) [latex]0.45[latex]
(C) [latex]0.5[latex]
(D) [latex]0.55[latex]
(E) [latex]0.6[latex]


10.  In a market, a dozen eggs cost as much as a pound of rice, and a half-liter of kerosene costs as much as [latex]8[latex] eggs. If the cost of each pound of rice is $[latex]0.33[latex], then how many cents does a liter of kerosene cost? [One dollar has [latex]100[latex] cents.]

(A) [latex]0.33[latex]
(B) [latex]0.44[latex]
(C) [latex]0.55[latex]
(D) [latex]44[latex]
(E) [latex]55[latex]


11. A father distributed his total wealth to his two sons. The elder son received [latex]3/5[latex] of the amount. The younger son received $[latex]30,000[latex]. How much wealth did the father have?

(A) [latex]15,000[latex]
(B) [latex]45,000[latex]
(C) [latex]60,000[latex]
(D) [latex]75,000[latex]
(E) [latex]89,000[latex]


12.  A bag contains [latex]6[latex] black chips numbered [latex]1-6[latex] respectively and [latex]6[latex] white chips numbered [latex]1-6[latex] respectively. If Pavel reaches into the bag of [latex]12[latex] chips and removes [latex]2[latex] chips, one after the other, without replacing them, what is the probability that he will pick black chip #[latex]3[latex] and then white chip #[latex]3[latex]?


13.  Tarik has a pile of [latex]6[latex] green chips numbered [latex]1-6[latex] respectively and another pile of [latex]6[latex] blue chips numbered [latex]1-6[latex] respectively. Tarik will randomly pick [latex]1[latex] chip from the green pile and [latex]1[latex] chip from the blue pile.

Quantity A Quantity B
The probability that both chips selected by Tarik will display a number less than [latex]4[latex] [latex]1/2[latex]



14.   A bag contains [latex]6[latex] red chips numbered [latex]1-6[latex] respectively and [latex]6[latex] blue chips numbered [latex]1-6[latex] respectively. If [latex]2[latex] chips are to be picked sequentially from the bag of [latex]12[latex] chips, without replacement, what is the probability of picking a red chip and then a blue chip with the same number?




1   D
2  C
3  Of the 21 pieces of fruit, 13 were pears.
4  $3
5  (a) $4,320 (b) $108
6 C
7 C
8 E
9 E
10 D
11 D