MAT (Stage-2) Mock Test

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MAT (Stage-2) Mock Test - 36

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Question 1
1 / -0

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

A
121

B
144

C
49

D
196

Solution
Question 2
1 / -0

A group consisting of 25 teachers, 20 engineers, 18 doctors and 13 salesmen visited a fair and spent Rs. 1330 altogether. It was found that 5 teachers spent as much as 4 engineers did, 12 engineers spent as much as 9 doctors did, and 6 doctors spent as much as 8 salesmen did. If every person in a professional group spent the same amount, then find the amount spent by each engineer.

A
Rs. 14

B
Rs. 17.50

C
Rs. 20

D
Rs. 21.25

Solution

Let the amounts spent by a teacher, an engineer, a doctor and a salesman be Rs. x, Rs. y, Rs. z and Rs. w, respectively.

Then, we have

5x = 4y, 12y = 9z and 6z = 8w
Question 3
1 / -0

A, B, C and D play a game of cards. A says to B, "If I give you 8 cards, you will have as many cards as C has and I shall have 3 cards less than C has. Also, if I take 6 cards from C, I shall have twice as many cards as D has." If B and D together have 50 cards, then how many cards does C have?

A
40

B
35

C
27

D
23

Solution

Clearly, we have
B + 8 = C ... (i)
A – 8 = C – 3 … (ii)
A + 6 = 2D … (iii)
B + D = 50 … (iv)
Putting C = A – 5, from (ii) into (i), we have
B + 8 = A – 5 or A – B = 13 ... (v)
Putting D = 50 – B from (iv) into (iii), we have
A + 6 = 100 – 2B or A + 2B = 94 ... (vi)
Solving (v) and (vi), we get
B = 27 and A = 40
∴ A has 40 cards and C has 35 cards.
Question 4
1 / -0

In a city, 40% of the adults are illiterate, while 85% of the children are literate. If the ratio of the number of adults to that of the children is 2 : 3, then what percent of the population is literate?

A
20%

B
25%

C
50%

D
75%

Solution

Let the numbers of adults and children be 2x and 3x, respectively.

Then, literate population = (100 – 40)% of 2x + 85% of 3x
Question 5
1 / -0

Among the passed students of a class, Amisha is twenty-second from the top and Sajal, who is 5 ranks below Amisha, is thirty-fourth from the bottom. The ratio of the students who passed the exam to those who failed is 4 : 1. How many students are there in the class?

A
60

B
75

C
90

D
Data inadequate

Solution

Amisha is 22^nd form the top and Sajal is 5 ranks below Amisha.
So, Sajal is 27^th form the top. Also, Sajal is 34^th from the bottom.
∴ Number of students passed = (26 + 1 + 33) = 60
Let the number of students passed and the number of failed students be 4x and x, respectively.
Then, 4x = 60 or x = 15
Hence, number of students in the class=(60 + 15) = 75
Question 6
1 / -0

In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every incorrect answer. If he attempts 60 questions and secures 130 marks, then the number of questions attempted correctly is

A
35

B
38

C
40

D
42

Solution

Let the number of questions attempted correctly be x.
Then, number of incorrect answers = (60 – x)
∴ 4x – 1(60 – x) = 130
⇔ 5x = 190
⇔ x = 38
Hence, the answer is (2).
Question 7
1 / -0

A man has a certain number of small boxes to pack into parcels. If he packs 3, 4, 5 or 6 boxes in a parcel, then one box is left over. If he packs 7 boxes in a parcel, then none is left over. What is the minimum number of boxes that he may have to pack?

A
106

B
301

C
309

D
400

Solution

Clearly, the required number would be such that it leaves a remainder of 1 when divided by 3, 4, 5, or 6 and no remainder when divided by 7. Thus, the number must be of the form (LCM of 3, 4, 5, 6)x + 1, i.e. (60x + 1) and a multiple of 7. Clearly, for x = 5, the number is a multiple of 7. So, the number is 301.
Hence, the answer is (2).
Question 8
1 / -0

An institute organised a fest, in which 1/5 of the girls and 1/8 of the boys participated. What fraction of the total number of students took part in the fest?

A
2/13

B
13/40

C
Data inadequate

D
None of these

Solution

We cannot determine the correct ratio until the total number of boys and girls is known.
Question 9
1 / -0

A truck can travel a distance of 232 miles on 14.5 gallons of gasoline. How many gallons of gasoline would the truck require to travel a distance of 400 miles?

A
25 gallons

B
27.5 gallons

C
16 gallons

D
64 gallons

Solution

Let the required number of gasoline be x gallons.
According to the question,
Question 10
1 / -0

A container of yogurt provides 6 grams of protein, which is 12% of the recommended protein intake per day. How much protein is recommended per day?

A
100 grams

B
50 grams

C
75 grams

D
125 grams

Solution

Let the protein recommended per day be n grams.
According to the question,
12% of n = 6
0.12 × n = 6
0.12n = 6
Or n = 50
Required amount of protein = 50 grams
Question 11
1 / -0

Diana's salary is $32,000 per year. If she spends $2880 per year on car payments, what percent of her salary is spent on the car payments?

A
9%

B
11%

C
13%

D
19%

Solution

Diana's salary is $32,000 per year and she spend $2880 on car payment per year.

Required % = 2880/32,000 × 100 = 9%
Question 12
1 / -0

Reena borrowed Rs. 1200 at simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?

A
3.6%

B
6%

C
18%

D
Cannot be determined

Solution
Question 13
1 / -0

An automobile company claims to be lending money at 10% simple interest, but they include the interest every six months for calculating the principal. What is the effective rate of interest?

A
10%

B
10.25%

C
10.5%

D
None of these

Solution

Let the principal be Rs. 100.

Interest for half year = 1/2 × 10 = 5%

So, net principal = 100 + 5 = Rs. 105

So, amount at the end of 1 year = Rs. (100 + 5 + 5.25)

∴ Effective rate = (110.25 - 100) = 10.25%
Question 14
1 / -0

A student has to get 40% of the total marks in order to pass an examination. Shivani secured 220 marks and failed by 20 marks. Calculate the total marks.

A
500

B
540

C
600

D
700

Solution

Marks to pass = 220 + 20 = 240
∴ 40% of the total marks = 240
Let the total marks be x.
40% of x = 240
Or x = 600
Total marks = 600
Question 15
1 / -0

If a man sells a shirt at Rs. 400, he will incur a loss of Rs. 75. At what price should he sell the shirt to make a profit of Rs. 50?

A
Rs. 475

B
Rs. 500

C
Rs. 525

D
Rs. 550

Solution

First case,
SP = Rs. 400
Loss = Rs. 75
So, CP would be SP + Loss.
= 400 + 75 = Rs. 475
Second case,
CP = Rs. 475
Profit = Rs. 50
SP = CP + Profit
SP = Rs. 475 + 50 = Rs. 525