M4maths Previous Puzzles

01 Jun 2016 Remainder

If X = (16^3 + 17^3 + 18^3 + 19^3), then X divided by 70 leaves a remainder of

OPtion

1) 0
2) 1
3) 69
4) 3
5) 54
6) 8
7) 5
8) 43
9) 17
10)62

Solution

X = ( 16^3 + 17^3 + 18^3 + 19^ 3 )
(a+b) is a factor of (a^3+b^3)
(16^3+19^3) is divisible by 16+19 = 35
(17^3+18^3) is divisible by 17+18 = 35
so,X = ( 16^3 + 17^3 + 18^3 + 19^ 3 ) has a factor 35
also, X = ( 16^3 + 17^3 + 18^3 + 19^ 3 )is an even no. (unit digit is 6+3+2+9= 0) so, X has a factor 2.
[since, E+O+E+O = E]
so, X is completely divisible by 35*2 = 70 & leaves a remainder 0.
Option 1)

Correct Option: 1 Best Solution (16)

31 May 2016 How many months

Radheshyam started a business with Rs.42000 and is joined afterwards by Subramanyam with Rs.72000. After how many month did Subramanyam join, if the profits at the end of the year are divided equally.

OPtion

1) 2 months
2) 3 months
3) 4 months
4) 5 months
5) 6 months
6) 7 months
7) 8 months
8) 9 months
9) 10 months
10)11 months

Solution

Suppose Subramanyam joined after x months/
Then, he invested the money for (12-x) months
Therefore
42000 * 12 = 72000*(12-x) or
x = 5

Option 4)

Correct Option: 4 Best Solution (10)

30 May 2016 Sequence

What is the next number of the following sequence.
68, 76.5, 91.8, 103.275, 123.93, .....

OPtion

1) 162.46
2) 145.265
3) 152.375
4) 159.175
5) 165.24
6) 165.245
7) 172.45
8) 184.26
9) 172.24
10)148.35

Solution

68
68/8 + 68 = 8.5+68 = 76.5 (Divide by last digit + number)
76.5/5 + 76.5 = 15.3+76.5 = 91.8
91.8/8 + 91.8 = 11.475+91.8 = 103.275
103.275/5 + 103.275 = 20.655+103.275 = 123.93
Similarly
123.93/3 + 123.93 = 41.31+123.93 = 165.24

Option 5)

Correct Option: 5 Best Solution (7)

27 May 2016 Profit and loss

On an article with marked price Rs.40000, a customer has a choice between three successive, 2 discounts of 20%, 20% and 10% and three successive discount of 40%, 5% and 5%. By choosing the better offer, he can save.

OPtion

1) 715
2) 1380
3) 1430
4) 1570
5) 1640
6) 690
7) 785
8) 975
9) 1050
10)Nothing

Solution

90% of 80% of 80% of Rs.40000 = 23040
95% of 95% of 60% of Rs.40000 = 21660
Saving = Rs.23040 - Rs.21660 = 1380

Option 2)

Correct Option: 2 Best Solution (13)

26 May 2016 Find the minimum value of x

A cuboid of dimension 7 cm * y cm * 15 cm is given. Find the minimum value of y so that at least two cones of maximum volume having some dimensions and a height of 15 cm, can be cut from this solid.

OPtion

1) 7 cm
2) 7.5 cm
3) 3 cm
4) 12.5 cm
5) 15 cm
6) 8.5 cm
7) 10.5 cm
8) 9 cm
9) 3.5 cm
10)11.5 cm

Solution

By using figure
For y to be minimum
Max volume cone will have a radius of 3.5 cm.
Thus, minimum value of x
= 7+3.5
= 10.5 cm
Option 7)

Correct Option: 7 Best Solution (1)

25 May 2016 Coded language

If in coded language
XMAT = 2/2
HPSX = 1/3
SIJM = 2/2
GCAR = 3/1
Then code for
LOYE = ?

OPtion

1) 1/4
2) 2/2
3) 3/1
4) 4/0
5) 0/4
6) 1/3
7) 4/1
8) 1/8
9) 2/7
10)1/7

Solution

Positions of X, M, A & T in English alphabet are 24, 13, 1 & 20.
Two numbers are not cancelled by any of the integer and two numbers are cancelled by any integer, hence code is 2/2,
similarly for others
Similarly positions of L, O, Y & E in English alphabet are 12, 15, 25, 5
One number is not cancelled by any integer and three are cancelled by any integer, hence code is 1/3.
Option 6)

Correct Option: 6 Best Solution (6)

24 May 2016 Correct statement

Which one statement is correct.
If x^2 + y^2 + z^2 - xy - yz - zx < 0

OPtion

1) x = y = z
2) x > y > z
3) x < y < z
4) x ≠ y = z
5) x = y ≠ z
6) x ≠ y ≠ z
7) x, y, z have negative values
8) any one of x, y, z is negative
9) any two of x, y, z are negative
10)Not possible

Solution

x^2 + y^2 + z^2 – xy - yz – zx < 0
=> 2x^2 + 2y^2 + 2z^2 – 2xy - 2yz – 2zx < 0
=> x^2 + y^2 - 2xy + y^2 + z^2 - 2yz + z^2 + x^2 - 2zx < 0
=> (x – y)^2 + (y – z)^2 + (z – x)^2 < 0
(x – y)^2 + (y – z)^2 + (z – x)^2 ,
This expression is the sum of three perfect square numbers and it is not possible to make this expression less than 0.

Option 10)

Correct Option: 10 Best Solution (15)

23 May 2016 Sequence

What is the next number of the following sequence
69, 915, 515, 511, 17, .......

OPtion

1) 815
2) 87
3) 98
4) 778
5) 645
6) 168
7) 78
8) 575
9) 578
10)518

Solution

69
69 = 9 (6+9) = 915 {last number (sum of all number)}
915 = 5 (9+1+5) = 515
515 = 5 (5+1+5) = 511
511 = 1 (5+1+1) = 17
Similarly
17 = 7 (1+7) = 78

Correct Option: 7 Best Solution (35)

20 May 2016 Find the height

A well with 14 m inside diameter is dug 8 m deep. The earth taken out of it has been evenly spread all around it to a width of 21 m to form an embankment. Find the height of the embankment.

OPtion

1) 49.2 cm
2) 53.3 cm
3) 61.4 cm
4) 39.6 cm
5) 32.5 cm
6) 52.6 cm
7) 46.6 cm
8) 62.3 cm
9) 58.4 cm
10)None of these

Solution

Volume of earth dug out = 22/7*7*7*8 = 1232 cm^3
Area of embankment = Pi (R^2 - r^2)
= 22/7 * (28^2 - 7^2)
= 22/7 * 35 * 21
= 2310 m^2
Therefore
Height of embankment 1232/2310 * 100 cm = 53.3 cm
Option 2)

Correct Option: 2 Best Solution (8)

19 May 2016 How many different ways

There are 5 Apple and 6 Orange. In how many different ways can a selection of fruits be made if all fruits of same kind are numbered with different tags.

OPtion

1) 2048
2) 1
3) 1024
4) 41
5) 30
6) 11
7) 510
8) 2047
9) 1026
10)1023

Solution

All the fruits are numbered with different tags, thus it can be considered that all fruits are different objects,
For each fruit, we have two choices- Either select the fruit or not
Hence total number of choices are 2*2*2…….11 times – 1 = 2047

Option 8)

Correct Option: 8 Best Solution (1)