M4maths Previous Puzzles

06 Apr 2016 Coded language

If in coded language
169524 = 80/1
426538 = 1440/7
398254 = 8640/31
413526 = 240/7
Then
245231 = ?

OPtion

1) 232/17
2) 236/13
3) 358/11
4) 465/19
5) 240/17
6) 197/7
7) 289/5
8) 477/43
9) 321/8
10)260/9

Solution

169524 =(1*6*9*5*2*4)/(1+6+9+5+2+4)
=2160/27 = 80/1
Similarly 245231=(2*4*5*2*3*1)/(2+4+5+2+3+1)
=240/17

Option 5)

Correct Option: 5 Best Solution (11)

05 Apr 2016 First negative term

Which tern of the series 27, 24, 21, 18, 15, ..... is the first negative term.

OPtion

1) 9
2) 7
3) 16
4) 11
5) 15
6) 14
7) 10
8) 13
9) 12
10)8

Solution

Here a = 27 and d = 24-27 = -3 (Series is AP)
Let nth tern of the given AP be the first negative tern
Then Tn < 0
=> (a + (n-1)d) < 0
=> (27 + (n-1)(-3)) < 0
=> (27 - 3n + 3) < 0
=> 30 - 3n < =
30 < 3n
3n > 30
n > 10
Therefore n = 11
Hence, the 11th tern is the first negative tern of the give AP.
Option 4)

Correct Option: 4 Best Solution (17)

04 Apr 2016 What is next

What is next
e, o, e, r, e,.....

OPtion

1) x
2) f
3) g
4) e
5) a
6) h
7) r
8) k
9) b
10)c

Solution

One = e (Taking last alphabet)
Two = o
Three = e
Four = r
Five = e
Similarly
Six = x

Correct Option: 1 Best Solution (10)

01 Apr 2016 Interest

Ravindra borrowed Rs.720 from Manish at 8% simple interest for 3 years and lent the same sum to Bablu at 21/2 % simple interest for 2 years. In the whole transaction, Ravindra.

OPtion

1) lost Rs.43.20
2) gained 12.60
3) lost Rs.21.60
4) gained Rs.43.20
5) lost Rs.24.40
6) gained Rs.21.60
7) lost Rs.12.60
8) gained Rs.24.40
9) Neither gained nor lost
10)None of these

Solution

Interest paid by Manish = Rs. 720*8*3 / 100 = Rs.172.80
Interest received by Manish = Rs. 720 * 21/2 * 2/100 = 151.20
Loss = Rs.172.80 - 152.20
Rs. 21.60

Option 3)

Correct Option: 3 Best Solution (7)

31 Mar 2016 Quadratic Equation

If (1 + Sqrt2) and (1 - Sqrt2) are the roots of the equation ax^2 + bx - 1 = 0, then find the values of a and b.

OPtion

1) Sqrt2, 1
2) -1, Sqrt2
3) -2, Sqrt2
4) 1, Sqrt2
5) 1, -2
6) 1, -3
7) 2, -1
8) 3, -1
9) -1, -2
10) 1, 2

Solution

Sum of roots = 1 + Sqrt2 + 1 - Sqrt2 = 2
Product of roots = (1 + Sqrt2)(1 - Sqrt2) = -1
Sum of roots = -b/a = 2
b = -2a
And product of roots = -1/a = -1
a = 1
b = -2
Option 5)

Correct Option: 5 Best Solution (7)

30 Mar 2016 Sides of the two squares

If the area of the larger square is subtracted from twice the area of the smaller square, then the result is 8 cm^2. However, if 3 times the area of the smaller square is added to 2 times the area of the larger square, then the result is 236 cm^2. Determine the side of the two squares.

OPtion

1) 8cm, 14cm
2) 2cm, 6cm
3) 4cm, 10cm
4) 2cm, 4cm
5) 4cm, 8cm
6) 6cm, 8cm
7) 8cm, 10cm
8) 6cm, 10cm
9) 8cm, 12cm
10)4cm, 6cm

Solution

Let the side of the smaller be x cm and side of the larger square be y cm. Then
According to the question, we get
2x^2 - y^2 = 8
=> y^2 = 2x^2 - 8 (i)
Also
3x^2 + 2y^2 = 236
By using (i)
x^2 = 36
x = + - 6 (Rejecting -6)
x = 6
Therefore x = 6
y^ = 64
y = 8
x(smaller) = 6, y(larger) = 8
Option 6)

Correct Option: 6 Best Solution (19)

29 Mar 2016 Coded language

If in coded language
4216 = 3
1211 = 4
9164 = 5
Then
1649 = ?

OPtion

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

Solution

Here 4216 contains 4, 1 & 16 (Total 3 numbers). All these numbers are perfect squares hence code is 3
Similarly
In 1649, there are 6 perfect square numbers. These are 1, 4, 9, 16, 64, 49

Option 2)

Correct Option: 2 Best Solution (2)

28 Mar 2016 Sequence

What is the next number of the following sequence.
486, 572, 644, 688, .....

OPtion

1) 710
2) 774
3) 760
4) 730
5) 786
6) 798
7) 732
8) 712
9) 704
10)776

Solution

486
486 + 86 = 572
572 + 72 = 644
644 + 44 = 688
Similarly
688 + 88 = 776

Option 10)

Correct Option: 10 Best Solution (39)

25 Mar 2016 Probability

A letter is chosen at random from the letters of English alphabet. Find the probability that it is a letter of the word 'DELHI'.

OPtion

1) 1/3
2) 5/13
3) 1/7
4) 2/13
5) 1/8
6) 5/26
7) 5/23
8) 1/13
9) 2/3
10)None of these

Solution

There are five letter in the word 'DELHI'
Therefore Number of favourable outcomes = 5
Total number of possible outcomes = 26 (Letter in English alphabet)
Therefore
Probability of getting a letter of the word 'DELHI' = 5/26

Option 6)

Correct Option: 6 Best Solution (12)

24 Mar 2016 Simple Interest

Rajendra invested 1/3 of his capital at 7%, 1/4 at 8% and the remainder at 10%. If his annual income is Rs.1122, the capital is

OPtion

1) 10800
2) 13800
3) 12000
4) 14400
5) 14200
6) 14800
7) 10400
8) 13200
9) 12800
10)8800

Solution

Let the capital be Rs.x Then,
x/3 * 7/100 * 1 + x/4 * 8/100*1 + 5x/12 * 10/100 * 1 = 1122
7x/300 + 8x/400 + 50x/1200 = 1122
102 x = 1122*1200
x= 1122*1200/102
x = 13200

Option 8)

Correct Option: 8 Best Solution (20)