# Common Problem Solving Practice Test 5

Question – 1

1. What is the remainder when x^8-x^7+x^6-x^5+x^4-x+1 is divided by x-1? Indicate the correct option.(Note: [x^2=x*x] )

• A. 0

• B. 1

• C. 2

• D. 3

• E. 4

Put x=1 in th polynomial.
1^8-1^7+1^6-1^5+1^4-1+1
= 1-1+1-1+1-1+1
= 1
Remainder = 1
Option B is correct.

Question – 2

2. A rectangular field is divided into 8 portions. Three different balls are thrown in the different sections such that there is only one ball in one section. How many different arrangements are possible? Indicate the correct option.

• A. 336

• B. 3

• C. 8

• D. 24

• E. 6720

3 balls can be put in 8 sections in P(8,3) ways.
P(8,3) = 8!/(8-3)!
= 8*7*6
= 336
Option A is true.

Question – 3

3. How many words can be formed by the letters of the word BALLOON? Indicate the correct option.

• A. 1260

• B. 420

• C. 900

• D. 5040

• E. 120

The word has 7 letters and 2 are repeated twice.
The number of words is given by 7!/(2!2!) = 7*6*5*4*3/2
=7*6*5*2*3
=1260
Option A is true.

Question – 4

4. Samuel has a pack of cards from which Ketan removes all the diamonds. Which of the following is the probability of Samuel’s drawing a king from the remaining pack? Indicate the correct option.

• A. 1/4

• B. 1/3

• C. 1/5

• D. 1/2

• E. 3/8

When all the diamonds have been removed, the remaining cards are 52-13=39 in number
The number of kings = 3
Probability = 3/39=1/3
Option B is true.

Question – 5

5. Which of the following is the area of a rhombus with diagonals 13m and 24m? Indicate the correct option.

• A. 156 sq.m

• B. 312 sq.m

• C. 624 sq.m

• D. 78 sq.m

• E. 45 sq.m

Area = 1/2(product of diagonals)
=1/2(13*24)
=13*12
=156 sq.m.
Option A is correct.

Question – 6

6. In twenty years from now, Tina will go from being thrice as old as Pam to being twice. What is the present age of Tina? Indicate the correct option.

• A. 20 years

• B. 30 years

• C. 40 years

• D. 50 years

• E. 60 years

Let the age of Pam today be x years.
Age of Tina= 3xAfter 20 years, Tina’s age will be (3x+20) and Pam’s (x+20)

According to conditions, (3x+20) = 2(x+20)
3x+20=2x+40
x=20

Tina’s present age =60 years
Option E is correct.

Question – 7

7. A cube of iron with each edge 12cm is recast into 27 equal cubes. What is the edge of each? Indicate the correct option.

• A. 1.5cm

• B. 2.5cm

• C. 3cm

• D. 4cm

• E. Cannot be determined

Volume of cube = 12*12*12
Volume of each cube = 12*12*12/27
= 4*4*4
Edge of each cube = 4cm
Option D is correct.

Question – 8

8. Kevin deposits \$10000 in a scheme at 5% simple interest. The interest is added to the principal every 5 years. In how many years will the amount become \$15625? Indicate the correct option.

• A. 20

• B. 15

• C. 2

• D. 5

• E. 10

Let the number of years be n.
Principal after 5 years = \$10000 + 10000*5*5/100
= 10000 + 2500=12500
Principal after 10 years = 12500 + 12500*5*5/100
= 12500 + 3125
= 15625
The time taken is 10 years.
Option E is correct.

Question – 9

9. The sum of two numbers is 12 and their product is 32. Which of the following is equal to the sum of the squares of the two numbers? Indicate the correct option.(Note: [x^2=x*x] )

• A. 44

• B. 35

• C. 80

• D. 90

• E. 56

Let the numbers be x and 12-x
x*(12-x)=32
12x-x^2=32
x^2-12x+32=0
x^2-8x-4x+32=0
x(x-8)-4(x-8)=0
x=4, 8
The two numbers are 4 and 8
Sum of their squares = 4^2+8^2=16+64
= 80
Option C is correct.

Question – 10

10. Which of the following is equal to (2/3)^4*(3/4)^2*(4/2)^3? Indicate the correct option.(Note: [x^2=x*x] )

• A. 3

• B. 8/9

• C. 72

• D. 1/72

• E. 9/8

(2/3)^4*(3/4)^2*(4/2)^3
= (2^4/3^4)*(3^2/4^2)*(4^3/2^3)
= (2^4*3^2*4^3)/(3^4*4^2*2^3)
=2^(4-3)*3^(2-4)*4^(3-2)
=2*3^(-2)*4
=2*4/3^2
=8/9
Option B is correct.

Question – 11

11. Which of the following is the rationalizing factor of 3+sqrt(3)? Indicate the correct option.

• A. 3 – sqrt(3)

• B. -Sqrt(3)-3

• C. Sqrt(3)+3

• D. 3+sqrt(3)

• E. 3*sqrt(3)

The rationaliing factor of 3+sqrt(3) is 3-sqrt(3).
Option A is correct.

Question – 12

12. For two right-circular cylinders the ratio of the radii is 2:3 and the ratio of their heights is 5:6. Which of the following is the ratio of their curved surface areas? Indicate the correct option.

• A. 3:5

• B. 1:3

• C. 5:9

• D. 4:7

• E. 4:9

Let their radii be 2x and 3x and their heights be 5y and 6y.
Curved surface area of a cylinder = 2*pi*r*h, where r and h are radius and height
Ratio of curved surface areas = 2*pi*2x*5y:2*pi*3x*6y
= 2x*5y:3x*6y
= 10:18
= 5:9
Option C is true.
[pi=22/7]

Question – 13

13. A machine produces K items in L seconds. How many items will it produce in 3/5 hours? Indicate the correct option.

• A. 6000K/L

• B. L/(6000K)

• C. K/(6000L)

• D. 2160K/L

• E. 2160L/K

Items produced per second = K/L
Items produced per minute = K/L*60
Items produced per hour = K/L*60*60
Items produced per 3/5 hours = K/L*60*60*3/5
= 2160K/L
Option D is correct.

Question – 14

14. The ratio of milk to water in three containers is 5:1, 3:1 and 5:2. The three containers hold equal quantities. These are emptied into a fourth container. What is the ratio of water to milk in the resulting solution? Indicate the correct option.

• A. 13:4

• B. 5:3

• C. 59:193

• D. 193:59

• E. 4:13

Quantity of milk per unit in first container = 5/(5+1)=5/6
Quantity of water per unit in first container = 1/(5+1)=1/6
Quantity of milk per unit in the second container = 3/(1+3)=3/4
Quantity of water per unit in the second container = 1/(1+3)=1/4
Quantity of milk per unit in the third container = 5/(5+2)=5/7
Quantity of water per unit in the third container = 2/(5+2)=2/7
Required ration = (1/6+1/4+2/7)/(5/6+3/4+5/7)
= (28+42+48)/(6*4*7)*(6*4*7)/(140+126+120)
= 118/386
= 59/193
Option D is true.

Question – 15

15. The difference between the simple interest and the compound interest on \$600 at 5% is \$1.50. For how many years was the amount invested? Indicate the correct option.

• A. 1

• B. 2

• C. 3

• D. 4

• E. 5

Let the time be t years.
CI-SI=1.5
600[(1+5/100)^t-1] – 600*5*t/100 = 1.5
400{(105/100)^t-1}-20t=1Putting t =1, we get
400(105/100-1)-20=400*5/100-20
= 20-20=0
Putting t=2, we get
400{(105/100)^2-1}-20*2=41-40=1
Hence, t=2
Option B is true.
[t^2=t*t]