MAT (Stage-1) Mock Test

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MAT (Stage-1) Mock Test - 77

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Weekly Quiz Competition

Question 1
1 / -0

Containers A, B and C have mixtures of milk and water in the ratios 1 : 5, 3 : 5 and 5 : 7, respectively and are filled to their full capacity. The capacities of the containers are in the ratio 5 : 4 : 5. Find the ratio of milk to water if the contents of all the three containers are mixed together.

A
52 : 95

B
51 : 110

C
53 : 115

D
35 : 97

Solution

Let the capacity of container A be 120V litres, that of B be 96V litres and that of C be 120V litres (As the containers are in the ratio 5 : 4 : 5)

Milk in container A = (1/6) × 120V litres = 20V litres

Milk in container B = (3/8) × 96V litres = 36V litres

Milk in container C = (5/12) × 120V litres = 50V litres

Total milk when the solutions are mixed together = (20V + 36V + 50V) litres = 106V litres
Total solution = (120V + 96V + 120V) litres = 336V litres
Thus, total water in solution = (336V - 106V) litres = 230V litres
Desired ratio = 106/230 = 53/115
Thus, the ratio is 53 : 115
Question 2
1 / -0

Three partners A, B and C invested Rs. 30,000, Rs. 40,000 and Rs. 50,000 in a business for 5, 7 and 12 months, respectively. Find the ratio of their profits at the end of the year.

A
4 : 9 : 11

B
15 : 28 : 60

C
3 : 7 : 10

D
None of these

Solution

Ratio of their profits = 30,000 × 5 : 40,000 × 7 : 50,000 × 12 = 15 : 28 : 60
Question 3
1 / -0

In what ratio must a 25% sugar solution be mixed with a 50% sugar solution to get a 40% sugar solution?

A
3 : 2

B
4 : 5

C
2 : 3

D
7 : 9

Solution

Let x litres of 25% sugar solution be mixed with y litres of 50% sugar solution in order to get a mixture of 40% sugar solution.

According to the given condition,

Simplifying, we get x : y = 2 : 3
Question 4
1 / -0

The number of students who took admission in an institute got increased by 15% this year. If 2645 enrolled this year, what was the number of students who enrolled in the last year?

A
2200

B
2250

C
2300

D
2350

Solution

Let the number of students enrolled in the last year be N.
The number of students enrolled this year = 115% of N = 1.15N
According to the question, 1.15N = 2645
N = 2300
Question 5
1 / -0

The number of people migrating from a country increased by 4% in 2004 with respect to the previous year. There would be a decrease of 3% if 2,100 less people had migrated. Find the number of people who migrated in 2003.

A
30,000

B
25,000

C
20,000

D
15,000

Solution

Suppose, people migrated in 2003 = x
After 4% increase, people migrated = 1.04x
If it decreased by 3%, then people migrated = 0.97x
From the question,
(1.04 - 0.97)x = 2,100
x = 30,000
Question 6
1 / -0

A and B together can do a piece of work in 10 days and A alone can do it in 15 days. In how many days can B alone do it?

A
15 days

B
20 days

C
25 days

D
30 days

Solution

Total time taken by A and B together to do the work = 10 days
Time required by A to do the work alone = 15 days
∴A and B together can do (1/10) of the work in one day and A can do (1/15) of the work in one day.
∴ The work which can be completed by B in one day = (1/10) - (1/15) = 1/30
So, B alone will take 30 days to do the work.
Question 7
1 / -0

Aman and Farhan can complete a work in 30 days. Aman works for 16 days and Farhan finishes remaining work in 44 days. In how many days will Farhan complete the work alone?

A
60 days

B
50 days

C
74 days

D
55 days

Solution

Let Aman's 1 day's work = x and Farhan's 1 day's work = y.

Then, x + y = 1/30 and 16x + 44y = 1

Solving these two equations, we get

x = 1/60 and y = 1/60

Farhan's 1 day's work = 1/60

Hence, Farhan alone will finish the whole work in 60 days.
Question 8
1 / -0

If - means + and × means ÷, then 5 ×2 + 3 - 7 ÷ 1 + 3 =

A
13.5

B
15.5

C
10.0

D
11.5

Solution

5 × 2 + 3 - 7 ÷ 1 + 3

means 5 ÷ 2 + 3 + 7 ÷ 1 + 3

= 2.5 + 3 + 7 + 3

= 15.5
Question 9
1 / -0

If + means ÷, - means +, ÷ means - and × means ×, then 5 + 1 ÷ 7 + 1 × 3 × 7 - 3 =

A
-123

B
-145

C
-139

D
-177

Solution

5 + 1 ÷ 7 + 1 × 3 × 7 - 3
= 5 ÷ 1 - 7 ÷1 × 3 × 7 + 3
= 5 - 7 × 3 × 7 + 3
= 5 - 21 × 7 + 3
= 5 - 147 + 3
= -142 + 3 = -139
Question 10
1 / -0

If + means -, - means ÷, ÷ means ×, and × means +, then which of the following equations is correct?

A
12 - 3 + 6 ÷ 7 + 3 = -41

B
3 + 7 - 6 + 8 ÷ 3 × 7 = 56

C
7 ÷ 7 + 7 - 1 + 5 = 11

D
3 + 9 ÷ 3 + 7 - 3 = 13

Solution

12 - 3 + 6 ÷ 7 + 3
= 12 ÷ 3 - 6 × 7 - 3
= 4 - 6 × 7 - 3
= 4 - 42 - 3
= -38 - 3
= - 41
Question 11
1 / -0

If + means ÷, × means -, ÷ means × and - means +, then 7 × 6 - 90 + 9 ÷ 8 equals

A
81

B
-89

C
23

D
None of these

Solution

7 × 6 - 90 + 9 ÷ 8
means 7 - 6 + 90 ÷ 9 × 8
= 7 - 6 + 10 × 8
= 7 - 6 + 80
= 7 + 74 = 81
Question 12
1 / -0

Which of the following two signs should be interchanged in the equation to make the equation correct?

(6 - 3) + (4 × 2 + 13) ÷ (7 × 2) = 21

A
+ and -

B
× and ÷

C
÷ and +

D
× and -

Solution

After interchanging × and -, we get
(6 × 3) + (4 - 2 + 13) ÷ (7 - 2)
= 18 + 15 ÷ 5
= 18 + 3
= 21
Question 13
1 / -0

Which of the following diagrams correctly represents the relationship between the following?

Cat, Dog, Animals

A

B

C

D

Solution
Question 14
1 / -0

The question below contains three elements. These three elements may or may not have some linkage. The group of the elements may fit into one of the diagrams (1), (2), (3) and (4). You have to indicate the diagram for the given group of elements.

Dogs, Cows, Pigeons

A

B

C

D

Solution

The given classes have no members in common.
Question 15
1 / -0

In the following question, select the diagram out of the four that best represents the relationship among the items given in the question.

Keyboard, Monitor, Mouse

A
(a)

B
(b)

C
(c)

D
(d)

Solution

Since the given classes have no members in common, so option (1) is correct.