Week-2 Selective Maths

Set S consists of 3 positive integers.

The average (arithmetic mean) of the integers in Set S is 7.

The median of Set S is 9.

What is the greatest possible value of the least integer in Set S?

A 1
B 2
C 3
D 4
E 5

x, y, and z are positive.

x = 3y = 5z

What is the ratio of (x + y) to (x + z)?

A 7 to 15
B 8 to 15
C 8 to 9
D 10 to 9
E 4 to 3

When n is divided by 6, the remainder is 2.

When n is divided by 7, the remainder is 3.

If n is greater than 1 200, what is the smallest possible value of n?

A 1 214
B 1 216
C 1 217
D 1 219
E 1 220

A jar contains 60 marbles.

Two-thirds of the marbles in the jar are either black marbles or white marbles.

There are more than twice as many black marbles as white marbles in the jar.

There are more than 12 white marbles in the jar.

How many black marbles are in the jar?

A 12
B 13
C 24
D 27
E 30

Marie has a total of 30 tokens, of which some are red and some are yellow.

The red tokens are worth 5 points.

The yellow tokens are worth 10 points.

The total points of all the tokens that she had is 180 points.

How many red tokens can she lose so that the average points (arithmetic mean) of the remaining token is 8 points?

A 4
B 12
C 15
D 20
E 24

A bargain cutlery store sells knives, forks, and spoons.

All knives are sold for the same price, all forks are sold for the same price, and all spoons are sold for the same price.

Six knives, 3 forks, and 2 spoons are sold for a total of $2.80.

Thirteen knives, 7 forks, and 6 spoons are sold for a total of $6.55.

What is the cost of one knife, one fork, and two spoons?

A. $0.80
B. $0.95
C. $1.20
D. $1.35
E. $2.25

Martin purchased red and green apples only.

Each red apple cost $1.70 and each green apple cost $1.90.

Martin paid a total of $14 for all the apples he purchased.

How many green apples did Martin purchase?

A 2
B 3
C 4
D 5
E 6

Simple annual interest is given as I = Prt, where I is the amount of interest, P is the principal amount, r is the interest rate, and t is the number of years the principal amount was invested.

Marco opened two new investment accounts.

Investment 1 earns 8 percent simple annual interest and Investment 2 earns 10 percent simple annual interest.

Marco invested $200 more in investment 2 than in investment 1.

The total amount of interest that the two investment accounts earned in the first year were $164.

He made no other transactions in the two accounts.

The amount of interest that Investment 2 earned in the first year was how many more dollars than the amount of interest that Investment 1 earned in the first year?

A $36
B $64
C $100
D $800
E $1 000

Line S has slope −2 and passes through the point (1, 4).

The slope of line T is three times the slope of Line S.

Line T passes through the point (0, 14).

What is the x-coordinate of the point of intersection of Line S and Line T?

A -3
B -2
C 2
D 3
E 6

Anna, Jenny, and Linda are among 7 people standing in a line.

In how many different ways can these 7 people be standing in line if Anna, Jenny, and Linda are in 3 consecutive places in the line?

A 120
B 720
C 864
D 1 440
E 5 040

A phone card charges a flat fee for the first minute of a phone call, plus an additional charge per each extra minute of the call.

Mike used the phone card to make an 11-minute call that costs 55 cents, and a 23-minute call that costs 97 cents.

How much does the phone card charge for the first minute of a call?

A 3 cents
B 7 cents
C 10 cents
D 16 cents
E 20 cents

Out of the 200 tourists on the tour, 30 percent can speak Italian and 40 percent can speak French.

If 25 percent of the tourists in the tour can speak French but not Italian, what percent of the tourists in the tour can neither speak Italian nor French?

A 45 percent
B 50 percent
C 65 percent
D 90 percent
E 95 percent

7x – 3y = 35

10x – 4y = 51

What is the value of x + y?

A 3
B 3.5
C 6.5
D 8
E 10

The passcode to a certain vault is composed of different digits chosen from the nine numbers 1, 2, 3 4, 5, 6, 7, 8, and 9.

What is the ratio of the number of 5-digit codes to the number of 4-digit codes?

A 2:1
B 3:2
C 5:1
D 5:4
E 6:1