# Common Problem Solving Practice Test 1

Question – 1

1. What least number should be subtracted from 2590 so that the remainder when divided by 9, 11 and 13 will leave in each case the same emainder 6? Which of the following statements is true? Indicate the corrrect option.

• A. 2

• B. 3

• C. 6

• D. 10

• E. 14

The remainder will be divisible by the LCM of 9, 11 and 13
LCM = 1287
1287*2=2574
2574+6=2580
2590-2580=10
Hence, the required number is 10.

Question – 2

2. Which is the smallest number by which 19404 should be multiplied to make it a perfect square? Indicate the correct option.

• A. 2

• B. 3

• C. 7

• D. 11

• E. 22

19404=2*2*3*3*7*7*11
19404 should be multiplied by 11 to make it a perfect square.
Option D is true..

Question – 3

3. If a/b = 1/5 which of the following is equal to (3a+2b)/(3a-2b)? Indicate the correct option.

• A. 13/5

• B. 91/25

• C. -91/25

• D. -13/7

• E. 7/5

(3a+2b)/(3a-2b) = (3a/b+2)/(3a/b-2)
= (3*1/5+2)/(3*1/5-2)
= (3/5+2)/(3/5-2)
= (3+10)/5/(3-10)/5
= 13/-7
=-13/7
Option D is true.

Question – 4

4. Find the next number in the series 12, 17, 23, 30, 38. Indicate the correct option.

• A. 48

• B. 43

• C. 47

• D. 51

• E. 45

17-12=5
23-17=6
30-23=7
38-30=8
Hence, consecutive numbers are added in the series.
The next number will be 38+9=47
Option C is correct.

Question – 5

5. The price of commodity A is \$5800 and it decreases at the rate of \$2 per three months. Commodity B costs \$4200 and it increases at the rate of \$8 per four months. How many years will it take for the two commodities to become equal in price? Indicate the correct option.

• A. 4.5

• B. 3.8

• C. 20

• D. 60

• E. 50

Price reduction of A in one year = 4*2 = 8
Price increase of B after one year = 3*8 = 24
Let the prices of the two commodities be the same after x years
5800-8x=4200+24x
5800-4200=24x+8x
1600=32x
x=50
Hence, it shall take 50 years.
Option E is correct.

Question – 6

(Note: [x^2=x*x] )

• A. a^2/4c

• B. -a^2/4c

• C. -a/2c

• D. a/2c

• E. c^2/4a

For the roots to be equal, the discriminant has to be zero.
c^2-4*a*b=0
c^2=4ab
b=c^2/4a
Option E is correct.

Question – 7

7. Alice can knit a sweater in 30 days, Laura in 20 days and Sandra in 60 days. How many days will they take to knit the sweater if they share their work? Indicate the correct option.

• A. 5

• B. 10

• C. 15

• D. 20

• E. 25

Work done by Alice in one day = 1/30
Work done by Laura in one day = 1/20
Work done by Sandra in one day = 1/60
Work done by them working together in one day = 1/20+1/30+1/60
= (3+2+1)/60
= 6/60=1/10
Time taken to compete the work = 10 days
Option B is correct.

Question – 8

8. A boat takes 6 hours to go downstream and upstream a certain distance. It takes 4 hours to travel twice the distance downstream. Which of the following is the ratio of the speed of the boat in still water to the speed of the river? Indicate the correct option.

• A. 3:1

• B. 1:3

• C. 5:3

• D. 3:5

• E. 7:9

Let the speed of the boat in still water be x and the speed of the river be y
Speed upstream = x-y
Speed downstream = x+y
Let the distance travelled be DTime = Distance/Speed
D/(x+y) + D/(x-y) = 6 and 2D/(x+y) = 4
Putting D/(x+y)=2 …(1) in the first relation, we get
2 + D/(x-y) = 6
D/(x-y) = 4 …(2)
From (1) and (2), we get

(x+y)/(x-y) = 4/2 = 2
x+y=2x-2y
x-2x=-2y-y
-x=-3y
x/y = 3/1

Option A is true.

Question – 9

9. Which of the following is equal to 2% of 22% of 222? Indicate the correct option.

• A. 97.68

• B. 0.2442

• C. 24.42

• D. 48.84

• E. 0.9768

2% of 22% of 222 = 2% of 22*222/100
= 2% of 48.84
= 0.9768
Option E is correct.

Question – 10

10. Which of the following is the average of the first 10 even numbers? Indicate the correct option.

• A. 20

• B. 15

• C. 10

• D. 5

• E. 18

The numbers are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20
Average = (2+4+6+8+10+12+14+16+18+20)/10
= 10

Question – 11

11. By what number should each of 15, 24, 51 and 87 be lessened so that the remainders are in proportion? Indicate the correct option.

• A. 1

• B. 2

• C. 3

• D. 4

• E. 5

Let the number be x
15-x:24-x=51-x:87-x
(15-x)(87-x) = (24-x)(51-x)
1305-15x-87x+x^2=1224-51x-24x+x^2
1305-1224=-75x+102×81=27x
x=3
The number is 3
[x^2=x*x].

Question – 12

12. Sam lent \$4000 to Pam for two years at 5% simple interest. After two years, he lent the complete amount to Ann for three years at 7%. What was the interest returned by Ann? Indicate the correct option.

• A. \$4924

• B. \$924

• C. \$400

• D. \$1324

• E. \$5324

Simple interest SI is given by SI =P*R*T/100, where P, R and T are principle, rate and time.
Amount returned by Pam = 4000+ SI
= 4000 + 4000*5*2/100
= 4000 + 400
= 4400
Interest returned by Ann after three years = 4400*7*3/100
= 924
Option B is correct.

Question – 13

13. How many terms are required at the least to add up to at least 100 in the series 3, 5, 7, 9 …? Indicate the correct value.

• A. 16

• B. 33

• C. 15

• D. 10

• E. 35

The series is an AP with the first term a = 3 and common difference 5-3=2
Let n terms as up to at least 100
Sum of n terms Sn = n/2[2a+(n-1)d]
100<=n/2[2*3+(n-1)*2]
100<=n/2[6+2n-2]
100<=n/2[4+2n]
100<=n(2+n)
n=10
At least 10 terms add up to at least 100 in the given series.

Question – 14

14. Annie and Simmi run a race of 2km. Annie beats Simmi by 30m. Simmi reaches the finish line 6 seconds after Annie does. How long did Annie take to complete the distance? Indicate the correct option.

• A. 9004 seconds

• B. 1900 seconds

• C. 19994 seconds

• D. 9994 seconds

• E. 9546 seconds

Time taken by Simmi to cover 30 m = 6 secSpeed of Simmi in m/s=30/6 = 5m/s
Time taken by Simmi to cover 2 km = Distance*speed
= 2000*5 = 10000 sec

Time taken by Annie to cover 2 km = 10000 – 6 seconds = 9994 seconds
Option D is correct.

Question – 15

15. A dishonest shopkeeper mixes water in acid to earn a profit. He sells acid worth \$5.4/litre at \$4.2/litre. If he initially had 14 litres of acid then how many litres of water did he add to it? Indicate the correct option.

• A. 1l

• B. 2l

• C. 3l

• D. 4l

• E. 5l

Let the quantity of water added be x litre.
Total quantity = (14+x) litre
As per the conditions, we have
(14+x)*4.2=14*5.4
58.8+4.2x=75.6
4.2x=75.6-58.8
4.2x=16.8
x=4
Option D is correct.