MAT (Stage-1) Mock Test

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MAT (Stage-1) Mock Test - 76

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following will replace the question mark (?) in the problem given below?

A
500

B
625

C
529

D
400

Solution

(5 + 6 + 9 + 10)² = 900; (4 + 3 + 5 + 3)² = 225. The missing number is (8 + 7 + 5 + 3)² = (23)² = 529.
Question 2
1 / -0

Which number will replace the question mark?

A
15

B
25

C
35

D
22

Solution

(6 + 4 + 8) + 2 = 20
Likewise, (6 + 5 + 12) + 2 = 25
Question 3
1 / -0

A printer starts printing the pages of a book beginning with 1 and uses 3193 digits in all. How many pages does the book have?

A
1074

B
1075

C
1076

D
1077

Solution

Total digits of single digit numbers = 9 digits
Total digits of two digit numbers = 2 × 90 = 180 digits
Total digits of three digit numbers = 3 × 900 = 2700 digits

According to the questions:

Number of pages = 999 + 76 = 1075
Question 4
1 / -0

A person crosses a 600-metre long street in 5 minutes. What is his speed in km per hour?

A
4.2

B
7.2

C
8.2

D
9

Solution
Question 5
1 / -0

A man buys a scooter for Rs. 1400 and sells it at a loss of 15%. What is the selling price of the scooter?

A
Rs. 1190

B
Rs. 1050

C
Rs. 1090

D
Rs. 1200

Solution

Cost price = Rs. 1400
SP = CP - Loss % of CP
Selling price = 1400 - 15% of 1400 = Rs. 1190
Question 6
1 / -0

A train, 130 metres long, travelling at a speed of 45 km/hr crosses a bridge in 30 seconds. The length of the bridge is

A
270 metres

B
235 metres

C
245 metres

D
220 metres

Solution
Question 7
1 / -0

How much time will it take for an amount of Rs. 900 to yield Rs. 81 as interest at 4.5% per annum of simple interest?

A
2 years

B
4 years

C
3 years

D
5 years

Solution

Principal = P = Rs. 900 and SI = Rs. 81

Time = ? and rate = 4.5%

Time = (100 × SI)/( P × R)

= (100 × 81)/( 900 × 4.5) = 2 years

Required time = 2 years
Question 8
1 / -0

A sum of money placed at compound interest doubles itself in 4 years. In how many years will it amount to 8 times?

A
4 years

B
6 years

C
5 years

D
12 years

Solution

Let Principal = Rs. 100
Amount = Rs. 200
Rate = r%
Time = 4 years
Now,
A = P × [1 + (r/100)]ⁿ
200 = 100 × [1 + (r/100)]⁴
2 = [1 + (r/100)]⁴ ... (i)
If sum becomes 8 times in the time n years, then
8 = [1 + (r/100)]ⁿ
2³ = [1 + (r/100)]ⁿ ... (ii)
Comparing equations (i) and (ii), we get
[1 + (r/100)⁴]³ = [1 + (r/100)]ⁿ
[1 + (r/100)]¹² = [1 + (r/100)]ⁿ
Thus, n = 12
Question 9
1 / -0

Vikas can cover a distance in 1 hour 24 min by covering 2/3 of the distance at 4 kmph and the rest at 5 kmph. What is the total distance?

A
6 km

B
7 km

C
8 km

D
5 km

Solution

Let total distance be x km.

Vikas covered 2/3 of x at 4 km/hr and 1/3 of x at 5 km/hr.

According to question, total time = 1 hour 24 min = 7/5 hour

⇒ x = 6 km

Total distance = 6 km
Question 10
1 / -0

Two trains starting at the same time from two stations 200 km apart and going in opposite directions cross each other at a distance of 110 km from one of the stations. What is the ratio of their speeds?

A
11 : 15

B
11 : 12

C
11 : 7

D
11 : 9

Solution

We know, total distance = 200 km
If both the trains crossed each other at a distance of 110 km, then one train covered 110 km and the other 90 km [110 + 90 = 200 km].
So, ratio of their speeds = 110 : 90
= 11 : 9
Question 11
1 / -0

The ratio of monthly income of A to that of B is 3 : 2 and their expenditures are in the respective ratio of 5 : 3. Each saves Rs. 1000 a month. Find the incomes of A and B.

A
A - Rs. 6000, B - Rs. 4000

B
A - Rs. 1500, B - Rs. 1000

C
A - Rs. 3000, B - Rs. 2000

D
A - Rs. 9000, B - Rs. 6000

Solution

Suppose monthly incomes of A and B be 3x and 2x, respectively.
According to question,
Income - Savings = Expenditure

9x - 3000 = 10x - 5000
On solving, we get:
x = 2000
Using values of x, we get:
A's income = Rs. 6000
B's income = Rs. 4000
Question 12
1 / -0

If I try to distribute some marbles equally among 6, 7, or 8 kids, I am left with the same number of marbles in each case of distribution. However, I can equally distribute them among 13 kids. What can be the minimum number of marbles that I may have with me?

A
168

B
182

C
169

D
156

Solution

Since the marbles can be distributed among 6, 7 and 8 kids leaving same number of leftover marbles in each case, let's find the LCM of 6, 7 and 8 = 168
Possible remainders can be 1, 2, 3, 4 and 5.
Suppose, I was left with 1 marble.
That means total marbles = 168 + 1 = 169
This is completely divisible by 13 as 169 is a multiple of 13.
No other remainder possibility satisfies the divisibility rule of 13.
Thus, total number of marbles = 169
Question 13
1 / -0

How many numbers less than 10,000 are divisible by each of the numbers 21, 36 and 66?

A
2

B
3

C
4

D
5

Solution

LCM of 21, 36, 66 = 2772
Multiples of 2772 less than 10,000 are: 2772, 5544 and 8316.
Question 14
1 / -0

The average daily wage of 8 men, 10 women and 2 girls is Rs. 280. If the average daily wage of the men is Rs. 10 more than that of the women and the average daily wage of the women is Rs. 10 more than that of the girls, then the average daily wage of the men is

A
Rs. 287

B
Rs. 280

C
Rs. 282

D
Rs. 286

Solution

Total daily wages = 280 × 20 = Rs. 5600
Let average daily wage of girls be Rs. x.
Average daily wage of women = Rs. (x + 10)
Average daily wage of men = Rs. (x + 20)
According to the given condition,
8(x + 20) + 10(x + 10) + 2x = 5600
20x = 5340
x = Rs. 267
Hence, average daily wage of men = Rs. (x + 20) = Rs. 287
Question 15
1 / -0

The average daily expenditure of Abha, Arya and Disha is Rs. 2000. If the average daily expenditure of Abha is Rs. 100 more than that of Arya and the average daily expenditure of Arya is Rs. 200 more than that of Disha, then the average daily expenditure of Abha is

A
Rs. 2400

B
Rs. 2200

C
Rs. 2130

D
Rs. 2133

Solution

Total expenditure = 2000 × 3 = 6000
Let average daily expenditure of Disha be Rs. x.
Average daily expenditure of Arya = Rs. (x + 200)
Average daily expenditure of Abha = Rs. (x + 300)
According to the given condition,
x + (x + 200) + (x + 300) = 6000
3x = 5500
x = Rs. 1833.3
Hence, average daily expenditure of Abha = 1833.3 + 300 = Rs. 2133.3 ~ Rs. 2133