M4maths Previous Puzzles

06 Jun 2013 Number

Ten's digit of a two digits number is greater by 7 than the unit's digit. Sum of the digits is 1/9 of that number. Find the number.

OPtion

1) 63
2) 97
3) 18
4) 79
5) 81
6) 27
7) 36
8) 48
9) 56
10) None of these

Solution

Let unit's digit be x and Ten's digit be y and Number 10y+x
Now according to the question
y=7+x (i)
x+y=1/9(10y+x) (ii)
Solving (i) and (ii)
we get y=8 and x=1
Number 10y+x = 10*8+1
81
option 5

Correct Option: 5 Best Solution (24)

05 Jun 2013 Linear Equation

For what value of C, the following system of linear equations has infinite number of solution:
Cx+3y-(C-3)=0 and 12x+Cy-C=0

OPtion

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

Solution

For Infinite number of solutions:
C/12=3/C=-(C-3)/-C
From first two
C^2=36 and from last two 3=C-3
Common solution is 6
option 6

Correct Option: 6 Best Solution (9)

04 Jun 2013 Problem

Find two numbers such that one third of greater exceeds one half on the lesser by 1, and one fifth of the greater added to one sixth of the lesser equals one half of the lesser.

OPtion

1) 15,9
2) 60,36
3) 30,18
4) 20,10
5) 50,25
6) 32,16
7) 28,12
8) 32,18
9) 46,26
10) None of these

Solution

Now, according to question
(1/3)x=(1/2)y+1 (let larger no x, smallest no y)
and (1/5)x+(1/6)y=(1/2)y
On solving (i) and (ii), we get x=30 and y =18
option 3

Correct Option: 3 Best Solution (11)

03 Jun 2013 Sequence Sequence

What is the next number of the following sequence
61,52,63,94,46,.....

OPtion

1) 25
2) 81
3) 36
4) 16
5) 18
6) 44
7) 68
8) 72
9) 49
10)None of these

Solution

4^2=16 61 (Reverse the number)
5^2=25 52
6^2=36 63
7^2=49 94
8^2=64 46
9^2=81 18

Correct Option: 5 Best Solution (0)

31 May 2013 average

Sum of 50 numbers is 490. If greatest number is 20 more than the least. Least number is 0 and repeated twice then the average of remaining 47 numbers will be

OPtion

1) 8
2) 9.5
3) 10
4) 12
5) 12.2
6) 12.5
7) 12.9
8) 13
9) 8.6
10) none of these

Solution

greatest number = 20
least number = 0 and repeated twice so sum of these three numbers = 20+0+0 = 20
so sum of 47 numbers = 490-20 = 470
so avg = 470/47 = 10

Correct Option: 3 Best Solution (0)

30 May 2013 product

What will be the product of differences of (8% of 8 and 7 % of 7) and (6% of 6 and 5 % of 5).

OPtion

1) 0.0105
2) 0.0115
3) 0.0120
4) 0.0125
5) 0.0130
6) 0.0145
7) 0.0150
8) 0.0155
9) 0.0165
10) none of these

Solution

8*8/100-7*7/100 = 0.64-0.49 = 0.15
6*6/100-5*5/100 = 0.36-0.25 = 0.11
product = 0.15*0.11 = 0.0165

Correct Option: 9 Best Solution (0)

29 May 2013 dictionary

rank of the word MARRIAGE in the dictionary of words formed by letters of the word MARRIAGE.

OPtion

1) 6328
2) 6459
3) 6492
4) 6578
5) 6612
6) 6656
7) 6758
8) 6834
9) 6945
10)none of these

Solution

total no of words = 8*7*6*5*4*3*2*1/2*1*2*1 = 10080
so rank of word MARRIAGE
= (10080/8)5+(1260/7)0+(180*2/6)4+(60*2/5)4+(24/4)3+(6/3)0+(2/2)1+1=6656

Correct Option: 6 Best Solution (0)

28 May 2013 selection

Number of methods of selecting 2 cards out of 52 playing cards will be

OPtion

1) 1320
2) 1324
3) 1326
4) 2652
5) 2640
6) 2648
7) 3020
8) 3120
9) 4356
10) none of these

Solution

52*51/2 = 1326

Correct Option: 3 Best Solution (0)

27 May 2013 sequence

2,15,119,951,7607,...
next number of the given sequence will be

OPtion

1) 60855
2) 56647
3) 75467
4) 54329
5) 79231
6) 58673
7) 91347
8) 45733
9) 41299
10) none of these

Solution

2*8-1 = 15
15*8-1 = 119
similarly

Correct Option: 1 Best Solution (0)

24 May 2013 expresssion

If 5x^2-3y^2=(11/2)*xy, then value of x:y is....
given that x and y are positive numbers.

OPtion

1) 1:2
2) 4:5
3) 3:4
4) 2:5
5) 11:2
6) 5:6
7) 3:2
8) 6:7
9) 7:8
10) None of these

Solution

5x^2-3y^2=(11/2)xy
10x^2-6y^2=11xy
(10x^2/y^2)-6=11x/y (Dividing each term by y^2)
let x/y=k
10k^2-11k-6=0
solve
k=3/2 or -2/5
Taking the positive value for k we get,
x/y=3/2
option 7

Correct Option: 7 Best Solution (19)