Solution:1
Assume x years have passed and y years to go Given (2/3)x=(4/5)y x=(3/2)(4/5)y=(6/5)y But x + y
= 99 So (6/5)y+y=99 Solving we get y = 45 years
Solution:2
Let us shift the path to the left hand side and top. This does not change the area of the lawn. Now
lawn area = (60 - x) (40 - x) for x = 3, we get lawn area = 2109.
Solution:3
Ans: A Going by the options, 35 = 8(4) + 3.
Solution:4
Ans: A Let x = 44444444,
(x+1)(2x3)(x2)+(x6)/x2
(2x2-x-3)(x-2)+(x-6)/x2
2x3-5x2-x+6+x-6/x2
2x3-5x2/x2
2x-5
Substituting the value of x in 2x - 5, we get 88888883
Solution:5
Maximum 3 men can be played which means there can be 0, 1, 2, 3 men in the team.
(5C011C11)+(5C111C10)+(5C211C9)+(5C311C8)=2256
Solution:6
A should be coded as 1+6 = G (it occurred for first time) B should be coded as 2+6 = H (it occurred for
first time) B Should be coded as 2 + 36 = 38 - 26 = 12 = L (it occurred for second time) Option D is
correct
Solution:7
X must be the center of the circle and 32 points are on the circumference. So Option A is correct
Number of diagnols of a regular polygon =
n(n3)2
So for a polygon of 32 sides, Number of diagnols = 464. Now the minimum distance between any
two points =
2r32=1156r
Now total lengh of all the distances from 32 points =
2r + Sum of the lengths of all the 464
diagnols.
Sum of the lengths of x to all the 32 points = 32 radius = 32r
But the 464 diagnols have 16 diameters connecting 2 oposite points connecting via center. So
Sum of the lengths of distances from point to point is clearly greater than sum of the length from
x to all 32 ponts. Option B is correct
Correct Option 3
Solution: 8
Sol: Their sum can be 3,4,6,8,9,12 For two dice, any number from 2 to 7 can be get in
(n-1) ways and any number from 8 to 12 can be get in (13 - n) ways. Then possible ways are 2 + 3 + 5
+ 5 + 4 + 1 = 20 possible cases. So probability is (20/36)=(5/9)
Solution: 9
Consider a two digit number of the form
where a and b are single digit whole numbers
Given:
Now
cannot be more than 118, else the number would become three digit. Also it cannot
be less than 28, else the number would become single digit.
Since,both a and b are integers,
also has to be an integer.
Thereby making
the square of an integer.
Hence we check at 100,81,64,49,36. ( values for
1.100-18 = 82.
Sum of digits = 8 + 2 = 10(Square root of 100).
2. 81 - 18 = 63
Sum of digits = 6 + 3 = 9 (Square root of 81).
3. 64 - 18 = 46
Sum of digits = 4 + 6 =10 (Square root of 100), which is not consistent with the given condition. We
will observe similar cases for 49 and 36.
Hence, only 2 numbers are possible: 82 , 63.
Solution: 10
Option B
Solution: 11
As A is 20% more efficient than B, If B's per day work is 100 units then A's 120. Both persons together
completes (100 + 120) units = 220 units a day. They took 60 days to complete the work. So total work
= 60 x 220 If A alone set to complete the work, he takes = 60220/120=110 days
Solution: 12
1
If n similar articles are to be distributed to r persons, x +x2+x ......x =n each person is eligible to take
any number of articles then the total ways are n+r1Cr1 In this case x +x +x ......x =10 in such a
case the formula for non negative integral solutions is n+r1Cr1 Here n =6 and r=10. So total ways
are 10+61C61 = 3003
Solution: 13
As efficiency is inversely proportional to days, If Father : son's efficiency is 5 : 1, then Days taken by
them should be 1 : 5. Assume, the days taken by them are k, 5k. Given that father takes 40 days less.
So 5k - k = 40 k = 10 Father takes 10 days to complete the work. Total work is 10 x 5 = 50 units. If
both of them work together, they complete 5 + 1 units a day. 6/day. To complete 50 units, they take
50/6 = 8 1/3 days
Solution: 14
Assume that he bought b, brown sharpeners and w, white sharpeners and the cost of brown
sharpener is x and white sharpener is x + 1
So w(x+1) + bx = 100
w + b = 18
b = 18 - w
Substituting in equation 1, we get w(x+1) + (18 -w)x = 100 so w + 18 x = 100
Take option 1: If white sharpners are 13, x = (100 - 13) /18 = 4.833
Option 2, If white sharpeners are 10, x = (100 - 10)/18 = 5 So white sharpeners cost is 6.
Option 3 Satisfies this condition.
Solution: 15
Let x ques were correct. Therefore, (26- x) were wrong 8x5(26x)=0 Solving we get x=10
Solution:16
Use fibonnacci series, with starting two terms as 1, 2. So next terms are 3, 5, 8, 13, 21, 34, 55, 89
Solution:17
If a man is Red, his mother must be red, his mothers brother also red but after marriage, he gets
converted to Brown
Solution:18
2^74 +2^2058+2^2n = K
2^74 +2^2058+2^2n = (237)2+22058+(2n)2
We try to write this expression as (a+b)2=a2+2ab+b2
Now a = 237, 2ab = 22058 and b = 2n
Substituting the value of a in 2ab, we get b = 2020
Solution:19
Assume the distance between the teeth is 1 cm. Then the circumference of first gear is 12 cm and the
second is 14 cm. Now LCM (12, 14) = 84. So to cover 84 cm, the first gear has to rotate 8412 = 7
rounds (the second gear rotates 84 / 14 = 6 rounds as it is bigger)
Solution:20
If he plucks 23, then only 18 grows the next day. This means total roses get decreases by 5. So after n
days assume the number of roses got decreased 185 where n = 37, then 4 roses left.
Solution:21
Time taken by A and B is in the ratio of = 3:2 Ratio of the Work = 2 : 3 (since, time and work are
inversely proportional) Total money is divided in the ratio of 2 : 3 and B gets Rs.3000
Solution:22
Let average of first 10 numbers is a. Then sum = 10a Average of last 10 nmbers also a. Then their sum
= 20a From the options B correct
Solution:23
Sol: A day has 24 hrs. Assume x hours have passed. Remaining time is (24 - x) 24x=15xx=20 Time
is 8 PM
Solution:24
Largest -> A
A
B
F T/F T/F
T/F F T/F
C
D
F
T/F
F
T/F
T
T/F
T/F
T/F
T/F T/F
T/F T/F
T/F T/F
F
F
F
T/F
T
From the above table, If we assume that A has the largest then A and C both are lying. Similarly if we
find the truth fullness of the remaining people, it is clear that E has the largest and C lied. (Only one F in
the last column)
Solution:25
24 kmph = 24100060=400 m / min In 4 minutes he covered 4 x 400 = 1600 m This is equal to the
perimeter 2 ( l + b) = 1600 But l : b = 3:2 Let l = 3k, b = 2k Substituting, we get 2 ( 3k + 2k ) = 1600
=> k = 180 So dimensions are 480 x 320
Solution:26
f (f(0)) + f(0) = 2(0) + 3 f(1) = 3-1 = 2,
f(1) = 2 f(f(1)) + f(1) = 2(1) + 3 f(2) = 5-2 = 3,
f(2) = 3 f(f(2)) + f(2) = 2(2) + 3 f(3) = 7-3 = 4,
f(3) = 4 .............. f(2012) = 2013
Solution:27
24m + 16w = 11600 12m + 37 w = 11600 Solving we get 12 m = 21w Substituting in the first
equation we get, 42w + 16 w = 11600 w = 200 M = 350
Solution:28
Maximum 3 men can be played which means there can be 0, 1, 2, 3 men in the team.
(5C011C11)+(5C111C10)+(5C211C9)+(5C311C8)=2256
Solution:29
FG is as large as possible and all the 7 numbers should be different. By trial and Error method, 9 + 8 +
7 + 6 + 5 = 355 is getting repeated twice. 9 + 8 + 7 + 6 + 4 = 344 is getting repeated 9 + 8 + 7 +
5 + 4 = 333 repeats 9 + 8 + 6 + 5 + 4 = 32 None of the numbers repeat in the above case and 32 is
the maximum number FG can have. The value of G is 2.
Solution:30
Volume =lbh = 652 = 60 cm3 Now volume is reduced by 19%. Therefore, new volume =
(10019)10060=48.6 Now, thickness remains same and let length and breadth be reduced to x% so,
new volume: (x1006)(x1005)2=48.6 Solving we get x =90 thus length and width is reduced by 10%
New width = 5-(10% of 5)=4.5
