M4maths Previous Puzzles

15 Nov 2021 inequalities

x+y+z=19
1 < x < 5, 4 < y <8, 10 < z < 14
How many outcomes are possible for integral values of x, y and z

OPtion

1) 1
2) 2
3) 3
4) 4
5) 5
6) 6
7) 7
8) 8
9) 9
10) none of these

Solution

according to the given conditions
possible values of x, y and z are
x = 2, 3, 4
y = 5, 6, 7
z = 11, 12, 13
so possible combinations are
(2, 5, 12), (2, 6, 11), (3, 5, 11)

Correct Option: 3 Best Solution (2)

11 Nov 2021 Missing Number

Fill in the missing number
3, 15, 35, 63, 99, 143, 195, …?

OPtion

1. 240
2. 225
3. 235
4. 242
5. 255
6. 266
7. 256
8. 278
9. 245
10. None of the above

Solution

2^2 - 1 = 3
4^2 – 1 = 15
6^2 – 1 = 35
8^2 – 1 = 63
10^2 – 1 = 99
12^2 - 1 = 143
14^2 – 1 = 195
16^2 – 1 = 255

Correct Option: 5 Best Solution (1)

10 Nov 2021 Discount

Find the true discount reckoning 3% p.a. simple interest on ₹1802 due in 2 years’ time.

OPtion

1. 104
2. 108
3. 98
4. 106
5. 110
6. 120
7. 102
8. 100
9. 115
10. None of the above

Solution

T.D. = (A X R X T)/(100 + R X T)
= (1802 X 3 X 2)/(100 + 3 X 2)
= ₹102.

Correct Option: 7 Best Solution (2)

09 Nov 2021 share

Ram invests ₹46500 in 6% stock at 93 and sells the stock when its price rose to ₹95. He invests the sale proceeds in 9% stock at 95. Find out the change in Ram’s income.

OPtion

1. 1250
2. 1400
3. 4500
4. 4700
5. 1500
6. 1450
7. 4550
8. 4750
9. 1550
10. None of the above

Solution

Income from first stock = (6/93 x 46500) = 3000
We have to find the amount realized on selling this stock.
Amount realized on selling 93 stock = 95
∴ Amount realized on selling 46500 stock = 95/93 x 46500 = 475000
This amount is invested in 9% stock at 95.
∴ Income from the second stock
= (9/95 x 47500) = 4500
Hence, increase in income
= (4500 - 3000) = 1500.

Correct Option: 5 Best Solution (1)

08 Nov 2021 Percentage

What per cent of 75 Kg is 25.5 Kg?

OPtion

1. 14
2. 38
3. 42
4. 25
5. 46
6. 36
7. 34
8. 33
9. 28
10. None of the above

Solution

Let x% of 75 Kg be 25.5 Kg.
Then, X% of 75 Kg = 25.5 Kg
X / 100 × 75 = 25⋅5
X = 25.5 x 100 / 75 = 34.
Hence, 25.5 Kg is 34% of 75 Kg

Correct Option: 7 Best Solution (2)

05 Nov 2021 Revenue

The tax on a commodity is diminished by 18% and its consumption increases by 13%. Find the effect on revenue

OPtion

1. 6.25%
2. 6.5%
3. 7.2%
4. 7.34%
5. 7.50%
6. 8.25%
7. 7.75%
8. 6.75%
9. 6.80%
10. None of the above

Solution

Since tax × consumption = revenue
∴ Net% change in revenue = {x + y - (xy/100)} %
=[ -18 + 13 - {(18 x 13) / 100}]%
= -7.34%
∴ The revenue decreases by 7.34%

Correct Option: 4 Best Solution (3)

04 Nov 2021 cost price

Manoj sells a machine for 65 thousand at a loss. Had he sold it for 80 thousand, his gain would have been 5 times the former loss. Find the cost price of the machine

OPtion

1. 70
2. 72
3. 65.8
4. 69.5
5. 68
6. 67.5
7. 72.6
8. 73.6
9. 77.5
10. None of the above

Solution

Manoj sells a machine for Rs 65 thousand at a loss.
Let the cost price be c.p
Loss = c.p - 65
Now, had he sold it for Rs 80 thousand, his gain would have been 5 times the former loss.
Thus, 80 - c.p = 5 (c.p - 65)
⇒ 6c.p = 405
⇒ c.p = 67.5 Lakhs

Correct Option: 6 Best Solution (2)

03 Nov 2021 Average

Find the average of squares of consecutive odd numbers from 1 to 31.

OPtion

1. 245
2. 314
3. 355
4. 366
5. 341
6. 326
7. 402
8. 385
9. 399
10. None of the above

Solution

The required average = n (n + 2) / 3
= 31 ( 31 + 2 ) 3
= 31 x 33 / 3
= 341.

Correct Option: 5 Best Solution (2)

02 Nov 2021 Simplification

Simplify the below equation: -
2.45 × 2.45 - 0.9 × 2.45 + 0.45 × 0.45

OPtion

1. 1
2. 3
3. 4
4. 2
5. 2.5
6. 2.4
7. 1.4
8. 1.6
9. 1.5
10. None of the above

Solution

Given expression
= 2.45 × 2.45 - 2 × 2.45 × 0.45 + 0.45 × 0.45
= (2.45)^2 - 2 × 2.45 × 0.45 + (0.45)^2
= (2.45 - 0.45)^2 [ a^2 - 2ab + b^2 = (a - b)^2 ]
= (2)^2 = 4.

Correct Option: 3 Best Solution (4)

01 Nov 2021 Distance

Nikhil goes to station at the speed of 6 Km/h and returns with a speed of 4 Km/h. If he takes 6 hours in all, find out the distance in Km between the village and the station.

OPtion

1. 6
2. 8
3. 8.4
4. 14.4
5. 12.5
6. 13
7. 13.5
8. 14
9. 10
10. None of the above

Solution

Here, S1 = 6, S2 = 4 and T = 6.
∴ The distance between the village and the station
= T (S1 S2/S1 + S2) = 6 {(6 X 4)/ (6 + 4)}
= 144 / 10
= 14.4 Km.

Correct Option: 4 Best Solution (4)