Q1. Consider two tumblers, the first containing one litre of water. Suppose you take one spoon of water out of the first tumbler and pour it into the second tumbler and after which you take one spoon of the mixture from the second tumbler and pour it back into the first tumbler. Which one of the following statements holds true ?
a) There is less coffee in the first tumbler than water in the
second tumbler.
b) There is more coffee in the first tumbler than water in the
second tumbler.
c) There is as much coffee in the first tumbler as there is
water in the second tumbler.
d) None of the statements holds true.
Ans. C
Q2. A
mother, her little daughter and her just born infant boy together stood on a
weighing machine which shows 74kgs. How much does the daughter weighs if the
mother’s weight is
46kg more than the combined weight of daughter and the infant and the infant
weighs 60% less than the daughter.
a) 9
b) 10
c) 11
d) None of these
Ans. B
Explain : Let daughter’s weight be x.
Also, Infant’s weight is 60% less than daughter i.e 0.4x
Mother’s weight :
(x + 0.4x + 46)
Total weight = x + 0.4x + (x+0.4x+46) = 74
2.8x = 28
x = 10
Q3.
How many positive integers less than 4300 of digits 0 – 4.
a) 560
b) 573
c) 574
d) None of these
Ans. C
Explain : Let daughter’s weight be x.
Also, Infant’s weight is 60% less than daughter i.e 0.4x
Mother’s weight :
(x + 0.4x + 46)
Total weight = x + 0.4x + (x+0.4x+46) = 74
2.8x = 28
x = 10
Q4.
100 students appeared for two different examinations 60 passed the first,50 the
second and 30 both the examinations. Find the probability that a student
selected at random failed in both the examination ?
a) 5/6
b) 1/5
c) 1/7
d) 5/7
Ans. B
Explain : Probability that a student selected failed in both exams :
100 – (60 + 50 – 30)/100
100 – 80/100
20/100
1/5
Q5. It
was the semester exam day, Vidhya caught the college bus. She enjoyed
travelling by bus. Moving at 6 mph, the bus took Vidhya to college at the right
time. She finished her exam and had a chit chat with her friends and suddenly
she realized that it was 6 pm and she had missed the college bus. She decided
to walk back home at 4 mph. What is her average speed for the day ?
a) 4 mph
b) 5 mph
c) 2.4 mph
d) 4.8 mph
Ans. D
Explain : Since distance is
constant,
Average speed is given by 2xy/x+y
So,
(2*6*4)/(6+4) = 48/10 = 4.8mph.
Q6. A
lady has fine gloves and hats of different colors in her closet 18 blue, 32 red
and 25 yellow. The lights are out and it is totally dark. In spite of the
darkness, she can make out the difference between a hat and a glove. She takes
an item out of the closet only if she is sure that it is a glove. How many
gloves must she take out to make sure that she has a pair of each color ?
a) 6
b) 8
c) 60
d) 59
Ans. D
Explain : If we consider that all the items are gloves.
Then, 32+25+2 = 59
Q7. A
triangle is made from a rope. The sides of the triangle are 25 cm, 11 cm and 31
cm. What will be the area of the square made from the same rope?
a) 280.8565
b) 280.5625
c) 281.5646
d) 282.5624
Ans. D
Explain : Length of the rope = 25+11+31 = 67cm
Side of the square = 67/4 = 16.75cm
Area of the square = (side of the square)^2 = 16.75^2
280.5625 cm^2
Q8.
There are 10 points on a straight line AB and 8 on another straight line AC
none of them being point A. how many triangles can be formed with these points
as vertices?
a) 680
b) 720
c) 816
d) 640
Ans. D
Explain : To form a triangle we need 3 points
Select 2 points from the 10 points of line AB & 1 from the 8 on AC
(10C2)*(8C1)
Select 2 points from the 8 points of line AC & 1 from the 10 on AB
(8C2)*(10C1)
Total number of triangles = s1 + s2 = 640
Q9.
Find the greatest number that will divide 148 246 and 623 leaving remainders 4,
6 and 11 respectively.
a) 20
b) 12
c) 6
d) 48
Ans. B
Explain : Greatest Such number :
HCF{(148-4), (246-6), (623-11))} = 12
Q10.
There are 5 letters and 5 addressed envelopes. If the letters are put at random
in the envelops, the probability that only 2 letters are in the correct
envelopes is :
a) 3/8
b) 1/12
c) 1/6
d) 4/9
Ans. C
Explain : Ways of putting 5 letters into 5 envelopes = 5! = 120
Only 2 letters are in the correct envelopes
Let ABCDE be the letters.
A and B alone are put in the correct envelopes.
No. of ways:
AB ECD
AB DEC
2 ways.
No. of ways of selecting 2 letters from 5 = 5C2 = 10
No. of ways in which 2 letters are put in correct envelopes = 10*2 = 20
So, Probability that only 2 letters are in the correct envelopes is :
20/120 = 1/6
Q11.
Average marks of a,b,c is 48. When d joins average becomes 47. e has 3 more
marks than d. Average marks of b,c,d,e is 48. What is the marks of a ?
a) 42
b) 43
c) 53
d) 56
Ans. B
Explain : a + b + c = 144 (48*3)
a + b + c + d = 188
d = 44
e = 47
b + c + d + e = 192
b + c = 101
b = 43
Q12. There are 20 persons sitting in a
circle. In that, there are 18 men and 2 sisters. How many arrangements are
possible, in which the two sisters are always separated by a man ?
a) 18! * 2
b) 17!
c) 17! * 2
d) 12
Ans. A
Explain : In a group, assume 1 man along with two groups.
So, they can be arranged in 17! ways as circular
Also, we have 18 options for choosing one man.
Same way, two sisters can be arranged in 2 ways :
making it 18! * 2
Q13.
A number plate can be formed with two alphabets followed by two digits with no
repetition. How many possible combinations can we get ?
a) 58500
b) 67600
c) 57850
d) 58761
Ans. A
Q14.
A lady has fine gloves and hats of different colors in her closet 18 blue, 32
red and 25 yellow. The lights are out and it is totally dark. In spite of the
darkness, she can make out the difference between a hat and a glove. She takes
an item out of the closet only if she is sure that it is a glove. How many
gloves must she take out to make sure that she has a pair of each color ?
a) 6
b) 8
c) 60
d) 59
Ans. D
Explain : It is not given that how many of these items are gloves and how many are hats,
if we consider that all the items are gloves then according to my opinion
32+25+2 = 59 gloves, she must take out to make sure she has a pair of each
color.
Q15.
Spores of a fungus, called late blight, grow and spread infection rapidly.
These pathogens were responsible for the Irish potato famine of the mid-19th
century. These seem to have attacked the tomato crops in England this year. The
tomato crops have reduced and the price of the crop has risen up. The price has
already gone up to $45 a box from $27 a box a month ago. How much more would a
vegetable vendor need to pay to buy 27 boxes this month over what he would have
paid last month ?
a) 27$
b) 18$
c) 45$
d) 486$
Ans. D
Explain : A month ago it was $27 and now it is $45, a
difference of $18 for a box. And 27 boxes are to be bought. The amount he would
have paid more than previous month
= 27 x 18 = 486
Q16.
A car manufacturer produces only red and blue models which come out of the
final testing area completely at random. What are the odds that 5 consecutive
cars of the same color will come through the test area at a time?
a) 1 in 16
b) 1 in 12
c) 1 in 32
d) 1 in 25
Ans. A
Explain : The odds that five consecutive cars of red color= 1/2*1/2*1/2*1/2*1/2=1/32
The odds that five consecutive cars of blue color= 1/2*1/2*1/2*1/2*1/2=1/32
The odds that five consecutive cars of same color = 1/32 + 1/32 = 1/16
Q17.
An athlete decides to run the same distance in 1/4th less time that she usually
took. By how much percent will she have to increase her average speed ?
a) 0.25
b) 0.5
c) 0.33
d) 0.2
Ans. C
Explain : (3/4)t=1
t=4/3=1+1/3
She will have to increase her speed by 33.333%
to run the same distance in 3/4s of the time hence 0.33 is the answer
Q18.
The letters in the word “PLACES” are permuted in all possible ways and arranged
in the alphabetical order. Find the word at 48 position.
a) AESPCL
b) ALCEPS
c) ALSCEP
d) AESPLC
Ans. D
Explain : Arranging in alphabetical order A, C, E, L, P, S
A _ _ _ _ _= 5! = 120 (more than 48)
A C _ _ _ _= 4! = 24
A E _ _ _ _= 4! = 24 (the remaining 4 letters can be arranged in
4! ways)
24+24=48 (we get the required number)
48 is the last word then as per dictionary the word will be
AESPLC
Q19.
A alone can do 1/4th of the work in 2 days. B alone can do 2/3th of the work in
4 days. If all the three work together, they can complete it in 3 days so what
part of the work will be completed by C in 2 days ?
a) 1/12
b) 1/8
c) 1/16
d) None of these
Ans. A
Explain : A can do the total work in : 8 days
B can do it in 6 days.
Let the total work be 24 units.
A = 24/8 = 3,
B = 24/6 = 4,
A + B + C = 24/3 = 8
So C = 1 unit.
In two days C will do 2 units which is 2/24th part of the total work. So 1/12th
part.
Q20.
In how many ways a team of 11 must be selected a team 5 men and 11 women such
that the team must comprise of not more than 3 men.
a) 1565
b) 2256
c) 2340
d) None of these
Ans. B
Explain : The team may consist of:-
0 men + 11 women
1 men + 10 women
2 men + 9 women
or 3 men + 8 women.
So Number of ways are = 11C11+5C1 * 11C10 + 5C2*11C9+5C3*11C8
= 2256 ways.
Q21.
Bablu alone can do a piece of work in 10 days. Ashu alone can do it in 15 days.
The total wages for the work in Rs.5000 .how much should Bablu be paid of they
work together for entire duration of the work
a) 4000
b) 3000
c) 5000
d) 2000
Ans. B
Explain : Bablu’s 1 day’s work =1/10
Ashu’s 1 day’s work = 1/15
Ratio of wages of A and B =1/10 : 1/15=3:2
Bablu’s share= (5000* 3/5)= Rs.3000
Q22.
Average of 3 numbers ABC is given as 48. Average of A,B,C,D is 46. Its given
that E is having 3 more than D, then Average of B,C,D,E is 45. What is the
score of A ?
a) 46
b) 47
c) 48
d) 49
Ans. B
Explain : A + B + C) = 48 * 3 = 144
(A + B + C + D) = 80 * 4 = 184
D = 184 – 144 = 40
E = D + 3 = (40 + 3) = 43 kg
(B + C + D + E )= (45 * 4) = 180
(B + C) = 180 – 43 – 40 = 47
A = 184 – 97 – 40 = 47
Q23.
Raj travels a part of journey by taxi paying 15 per km and rest by train paying
21per km. If he travels a total of 450 Km and pay Rs.8130 then the distance
travelled by raj in train ?
a) 230
b) 260
c) 190
d) 180
Ans. A
Explain : Let the distance traveled by train = p
Distance travelled by taxi = (450-p)
Now, (450-p)15
+ p21=8130
On solving p=230
Q25.
A boy buys 18 sharpeners (brown or white) for Rs. 100. For every white
sharpener, he pays one rupee more than the brown sharpener. What is the cost of
white sharpener & how much did he buy ?
a) 5, 13
b) 5, 10
c) 6, 10
d) None of these
Ans. C
Explain : Let boy bought p white sharpeners @ Rs (q+1) and
(18-p) brown
sharpeners @ Rs q per sharpener, then
p(q+1)+p(18-p)=100
p= 100-18q
Only integral value of p less than 18 will be
10.
then p=10, q=5
so he bought 10 white sharpeners @ Rs 6 per
sharpeners and 8 brown
sharpeners @ Rs 5 per sharpener.
Ans is 6,10
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