36 HOUR PLACEMENT CLASS SHEET
QUANTITATIVE APPTITUDE
1
NUMBER THEORY, NUMBER SERIES,
RATIO PROPORTION, ALLEGATION MIXTURE,
Problems on ages & averages
1.
2.
3.
4.
LCM of 24, 36 and a third number is 2016
and their GCD is 4. What is the smallest
possible value of the third number?
a) 36
b) 224
c) 324
d) 216
Find the remainder when 22225555+55552222 is
divided by 7
a) 1
b) 3
c) 0
d) 5
What is the difference between the largest
and the smallest 4-digit number that can be
formed with the digits 0,7,8 and 9 without
repetition
a) 5683
b) 2781
c) 3820
d) 5432
If N chocolates are divided among 6 boys,
each gets an equal number of chocolates.
Find W, if it is a perfect cube and is by the
first three perfect squares?
a) 216
b) 324
c) 624
d) 625
c)
9.
6.
7.
8.
Three alarms ring at intervals of 2,6,12
minutes respectively. If they all ring together
at 1 PM when will they ring all together the
next time.
a) 1 AM
b) 1.12 PM
c) 1.12 AM
d) Next 1 PM
In a division, the quotient and the remainder
are two and four less than the divisor
respectively. If the number is 178, what are
the quotient and the divisor
a) 16,21
b) 12,14
c) 14,12
d) 21,16
Which of the following is exactly divisible by
all prime numbers between 10 and 20?
a) 75294
b) 46189
c) 35273
d) 48391
What is the least number that should be added
to 37301 so that it is exactly divisible by 27?
a) 21
b) 6
d) 13
If n2 is perfect cube, then which of the
following statements is always true?
a) n is odd
b) n is even
c) n3 is perfect square d) n is a perfect cube
10. What is the minimum number of identical
square tiles required to floor a room
measuring 10.8m × 9m?
a) 64
b) 72
c) 30
d) 48
11. 1000! ends with _________ number of
consecutive zeros
a) 248
b) 249
c) 312
d) 124
12. Simplify:
a)
c)
5.
14
17⁄
6
7⁄
2
1
1
1
3 2
5
3
4 7
1
1
3
3 2
2
3
4
5
b) 10⁄3
d) 23⁄7
13. What comes in the place of x in the following
question? 89.4 × 412.8 × 648.1 = 16x
a) 41.8
b) 16.2
c) 18.4
d) 25.6
14. If k+2 is a four digit odd number, then which
among the following must be a four digit
even number
a) k+1
b) k-1
c) k+3
d) More than one of above
15. If x+y+z is a positive number, then which of
the following cannot be true?
a) x<0<y<z
b) y<0<x<z
c) z<x<y<0
d) x<y<z
16. 120 apples were present with total of 7
persons. Each person had atleast 13 apples.
The number of apples with each is distinct.
Which of the following cannot be the total
number of apples with any 2 persons.
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36 HOUR PLACEMENT CLASS SHEET
a)
c)
47
27
b) 44
d) 33
17. Numbers from 1 to 100 are written side by
side. What is the 74th digit?
a) 3
b) 4
c) 1
d) 5
18. If a:b = 3:5 and a:c = 5:7, What is the value
of b:c?
a) 3:7
b) 21:35
c) 21:25
d) 25:21
19. A classroom has 4 boys and 6 girls. During
January, the same number of boys and girls
joined the classroom. How many members
does the classroom have now if the ratio of
boys to girls is 3:5?
a) 12
b) 13
c) 18
d) 20
20. The ratio of the number of blue balls to red
balls to yellow balls to green balls on a basket
is 4:7:6:8. What percent of the basket are red
balls?
a) 16%
b) 24%
c) 25%
d) 28%
21. If 16 kg of rice costing Rs.20 per kg is mixed
with x kg of rice costing Rs.30 per kg to
result in a mixture costing Rs.25 per kg, Find
x?
a) 14
b) 16
c) 18
d) 20
22. The average weight of a class of 20 student is
52 kg. If another student 40 kg weighing,
joins the class. What is the average weight of
the class?
a) 52
b) 54
c) 50.57
d) 51.43
23. In what ratio should 2 varieties of rice costing
Rs.20/kg and Rs 24/kg be mixed so that when
sold at Rs.27.60 kg a profit of 20% is made?
a) 1:2
b) 2:3
c) 1:3
d) 3:1
24. The sales recorded by saleem, a salesman, in
6 days of a week, were as follows? Rs.10,000
per day on the first 3 days, Rs.8000 on
Thursday, Rs.12,000 each on the next 2 days.
Find his average sales per day
QUANTITATIVE APPTITUDE
2
a)
c)
Rs.11333.33
Rs.10333.33
b) Rs.10666.67
d) Rs.10330
25. The ratio of the number of girls to that of
boys in a class is 2:3. If the average weight of
the boys in the class is 40 kg and that of the
class is 38 kg. Find the average weight of the
girls.
a) 35 kg
b) 36 kg
c) 38 kg
d) 34 kg
26. The average of A,B and C is 20. A is as much
more than the average as B is less than the
average. Find C
a) 15
b) 30
c) 25
d) 20
27. The average of 71 numbers is 48. If the
average of the first 59 is 46 and that of the
last 11 is 52. Find the 60th number?
a) 112
b) 132
c) 142
d) 122
28. The average age of PQRS. 5 years ago, was
45 yrs. By including T, the present average
age of 5 people is 49 years. Find the age of T,
5 years hence.
a) 40 yrs
b) 50 yrs
c) 55 yrs
d) 60 yrs
29. If a+b = 3 (c+d), which of the following is the
average of a,b,c and d?
a) c  d
b) 3  c  d 
4
8
c

d
c) c + d
d)
2
30. Four years ago the average age of A and B
was 19 years with C joining them, now the
average becomes 22 years. How old is C
now?
a) 20 years
b) 25 years
c) 28 years
d) 30 years
31. Ramu was twice as old as Rahim, 3 years
ago. After 3 years Ramu will be 4/3 times
Rahim age. Find Ramu’s present age in
binary numbers
a) 100
b) 110
c) 1001
d) 1100
32. Present ages of Shyam and Rasin are in the
ratio 5:4 respectively. Three years hence,
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36 HOUR PLACEMENT CLASS SHEET
ratio of their age will become 11:9
respectively find Rasin’s present age in years.
a) 15
b) 6
c) 24
d) None of these
33. Rita’s mother is twice as old as her brother.
Her brother is 5 years older than Rita. In 5
years her mother will be three times as old as
Rita is now. What is Rita’s present age
a) 20
b) 25
c) 15
d) 4
34. After 8 years Sita will be twice her age, she
was five years ago, Find her present age?
a) 18
b) 12
c) 16
d) 21
35. A father said to his son, ”I was as old as you
are at the present at the time of your birth”. If
the father’s age is 38 years now, the son’s age
five years back was
a) 14 yrs
b) 19 yrs
c) 33 yrs
d) 38 yrs
3
QUANTITATIVE APPTITUDE
42. 49, 1625, _____, 6481
a) 1628
c) 348
b) 3649
d) 642
43. 43, 47, 90, 56, 63, 119, 67, 79, _____
a) 150
b) 390
c) 270
d) 146
44. Find out the wrong number in the series
4443, 2423, 4322, 4511, 6221
a) 4443
b) 2423
c) 4322
d) 4511
e) 6221
45. Find the wrong number 3, 5, 12, 38, 154, 914
a) 5
b) 38
c) 154
d) 914
e) 12
46. 40, 20, 100, 50, _____, 125
a) 230
b) 329
c) 250
d) 312
36. How old is Priya now?
I) Three years ago, the average of Chitra
and Sheena was 18 years.
II) With Priya joining them, the average
becomes 22 years
a) Only (I)
b) Only (II)
c) Either (I) or (II) d) Neither (I) nor (II)
e) Both (I) & (II)
37. 12, 32, 72, 152, x
a) 312
c) 515
b) 325
d) 613
38. 1, 2, 5, 12, 27, 58, 121, _____
a) 246
b) 247
c) 248
d) 249
39. 225, 336, 447, _____, 669, 7710
a) 114
b) 338
c) 558
d) 991
40. (2,3), (3,5), (5,7), (7,11), (11,13)
a) 13,15
b) 15,16
c) 13,17
d) 13,19
41. 11, 10, _____, 100, 1001, 1000, 10001
a) 101
b) 110
c) 111
d) None
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36 HOUR PLACEMENT CLASS SHEET
QUANTITATIVE APPTITUDE
4
NUMBER THEORY
1.
By prime factorization,
24 = 23 × 3
36 = 22 × 32
LCM = 2016 = 25 × 32 × 7
The third number should at least (25 × 7) as
factors, Since the third number takes the
smallest possible value.
Therefore, third number = 25 × 7 = 224
2.
We know 2222  3
7
22225555 35555
So,

7
7
7 is co-prime of 3 so,
From FERMAT’S LITTLE theorem,
5555 6 
35555 3
So,

7
7
35 243

7
7
=5
3.
4.
5.
6.
Let the divisor be x
Quotient = x – 2, Remainder = x – 4
By the rule of division,
Divisor x Quotient + Remainder = Number
x(x – 2) + x – 4 = 178
 x2 – 2x + x – 4 = 178
 x2 – x – 4 = 178
 x2 – x – 182 = 0
 x = 14 or -13
∴ Divisor = 14 & Quotient = 12
7.
Prime numbers between 10 & 20 are 11,13,17
& 19
46189 is the only number which is
divisible by all 11,13,17 & 19.
8.
1381
27 37301
27
103
81
220
216
41
27
14
The largest four digit number that can be
formed with the digits 0,7,8 & 9 is 9870 and
the smallest four digit number that can be
formed with the digit is 0,7,8 & 9 is 7089.
So, the difference is
9870
- 7089
2781
=> 2781
N is a multiple of 6 and divisible by the first
three perfect square i.e., 1,4 & 9. Least
possible number must be a multiple of 36 & a
perfect cube
So, 36 × (6) = (6)3
= 216
2,6,12 are the intervals
2
3
2
So, 14 is the remainder.
If we add 13 to that we get 27 which is
exactly divisible by 27.
So, 13 is the answer.
9.
n2 = perfect cube.
For eg.:- n=8
(8)2 = 64
Where, 64 is a perfect cube of ‘4’.
From the given statement, statement ‘d’ is
always true since “8 is perfect cube of 2”.
10. Ans : c
10.8m × 9m
Largest number that divides 10.8 & 9 is 1.8
10.8 ×9
So number of tiles required =
1.8 ×1.8
= 30
2, 6, 12
1, 3, 6
1, 1, 2
1, 1, 1
2 × 3 × 2 = 12
So, at 1 pm = 1.12 pm
11. 1000!=1000×999×998×…...×4×3×2×1
Number of zeros ending the number
represented by,
n! = (n/5) + (n/52) + (n/53) …. (n/5x).
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36 HOUR PLACEMENT CLASS SHEET
where, 5x≤ n.
1000
1000
1000
1000
(
)+(
)+(
)+(
).
5
25
125
625
=> 200 + 40 + 8 + 1
=> 249
12.
10 9 13

3 4 5
10 9 36

3 4 7
39
2

13 36

12 7
39 7
 
2 39
=
QUANTITATIVE APPTITUDE
5
We get 45.so, maximum amount of apples for
2 is 45.so, it can’t be 47.
17. When numbers from 1 to 9 are written side
by side it takes up 9 digits.
From 11 to 30 totally there are (20×2)
= 40 digits.
From 31 to 40 there are 20 digits.
From 41 to 42 there are 4 digits.
So totally till 42 there are 73 digits.
So 74th digit is 4.
18.
7
2
13. 89.4 × 412.8 × 648.1 = 16x.
(23)9.4× (22)12.8× (26)8.1 = (24)x.
228.2 × 225.6 × 248.6 = 24x
2(28.2 + 25.6 + 48.6) = 24x
102.4 => x = 25.6
2102.4 = 24x => x =
4
14. k + 2 = 4-digit odd number.
For eg : k = 2465.
k + 2 => 2467 => 4-digit odd number.
If k +1 => 2465 + 1 = 2466 => 4-digit even
number.
If k – 1 => 2465 – 1 = 2464 => 4-digit even
number.
If k + 3 => 2465 + 3 = 2468 => 4-digit
even number.
All three satisfies.
15. x + y + z is a positive number.
If x < 0 < y < z, here x + y + z is a +ve
number.
In y < 0 < x< z, here, x , z are greater than
‘0’, so, x + y + z is a +ve number.
In z < x < y < 0, here all x , y, z are less than
‘0’, x + y + z cannot be a +ve number.
In x < y < z, x + y + z is a +ve number.
So, z < y < x < 0 cannot be a +ve number.
16. Lets say they have these number of apples.
13, 14, 15, 16, 17, 18, 19. The sum is 112
(so, 112 < 120).
So, we have still 8 apples remaining.
To make the sum maximum, we assume to
give 19 apples to make a sum of 27.
Now, if we add 27 to 18(2nd biggest).
𝑎
3
𝑏
5
𝑏
𝑎
5
5
25
= , = , so, b : c = × = × =
5 𝑎
3
𝑎
𝑐
3
7
21
b:c = 25:21
a:b = 3:5 = 15:25 &
a:c = 5:7 = 15:21
so, when a = 15, b = 25, we get c = 21.
b:c = 25:21
𝑏
19. If x boys & x girls joined the classroom.
Then, the new ratio of boys to girls would be
(4+x) : (6+x).
4+𝑥
3
so,
= => (4+x)5 = (6+x)3
6+𝑥
5
20+5x = 18+3x
2x = 2 => x = 1.
1 boy & 1 girl joined the other 4 boy & 6
girl, a total of 12.
20. The fraction of the basket that is red balls is,
7
7
= and
4+7+6+8
7
25
25
× 100% => 28%
21. 20 per kg = 16 kg of rice.
30 per kg = x kg of rice.
20(16)
30(16)
25
5
5
1:1 => ∴ 16 kg of rice costs Rs.30 per kg.
22. Avg of 20 students = 52.
∴ 52×20 = 1040.
One student = 40kg ∴ 1040+40 = 1080
1080
The avg weight of class =
21
= 51.43
23. 27.60 kg → profit of 20%
120
x×1.2 = 2760 => x ×
= 27.60
100
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36 HOUR PLACEMENT CLASS SHEET
x=
2760
120
29. The avg is,
= 23.
20
𝑎+𝑏+𝑐+𝑑
24
=>
23
1
3
=> 1:3
24. 10,000 per day (3 days)
8,000 on Thursday (1 day).
12,000 on (2 days).
30000+8000+24000
∴ Average sales per day =
=
25. C =
38 =
62,000
6
6
= 10333.33
𝑎 ×𝑚+𝑏 × 𝑛
𝑎+𝑏
40 ×3+𝑥 ×2
5
 120 + 2x = 190
 2x = 70
 x = 35.
26. Average of A,B& C is 20.
A is as much more than avg = A-20.
B is as much less than avg = 20-B.
A-20 = 20-B.
A + B = 40.
𝐴+𝐵+𝐶
= 20.
3
40+𝐶
3
QUANTITATIVE APPTITUDE
6
= 20 => 40 + C = 60
C = 20
27. Avg of 71 numbers = 48
Avg of 59 numbers = 46
Avg of 11 numbers = 52
60th = (71 × 48) - {(59 × 46) + (11 × 52)}
= 3408 – (2714 + 572)
= 3408 – 3286
= 122
28. P, Q, R, S avg age is 45 years
∴ 45 × 4 => 180
5 years ago => 180 + 25
= 205 (PQRS present age)
After T, the average age of 5 people
=> 49 × 5
= 245
The age of T => 5 years hence
= 245 – 205
= 40 years
= 40 + 5 (∴ 5 years hence)
= 45 years
=
4
3𝑐+3𝑑+𝑐+𝑑
4
3(𝑐+𝑑)+𝑐+𝑑
=
4
4𝑐+4𝑑
4
= c+d
30. Average age of A & B is,
19 => 4 years ago
𝐴+𝐵
∴
= 19
2
A + B = 38, As 4 years ago,
38 + 4 + 4 = 46
Now, Avg of A, B & C = 22 years
𝐴+𝐵+𝐶
∴
= 22
3
A + B + C = 66
66 – 46 = 20
Age of c = 20
31. 3 years ago
Rahim = x
Ramu = 2x
Present age
Rahim = x + 3
Ramu = 2x + 3
After 3 years,
Rahim = x + 6
Ramu = 2x + 6
4
2x + 6 = ( ) (x + 6)
3
6x + 18 = 4x + 24
2x = 6
x=3
=>100 in binary
32. Present age of shyam & Rasin
5:4
5𝑥+3
11
=
4𝑥+3
9
9(5x + 3) = 11(4x+3)
45x +27 = 44x+33
x =6
Rasin present age => 4x
= > 4 × 6 = 24
33. Rita = x
Rits’s brother = x+5
Rita’s mother = 2(x+5)
Rita’s mother after 5 years
=> 2(x+5) + 5 = 3x
2x + 10 + 5 = 3x
x =15
34. Sita’s present age = x
5 years ago = x-5
8 years later => (x+8) = 2(x-5)
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36 HOUR PLACEMENT CLASS SHEET
x+8 = 2x-10.
x = 18
7
QUANTITATIVE APPTITUDE
45. 3×1+2=5,
5×2+2=12,
12×3+2=38,
38×4+2=154, 154×5+2=772, 772×6+2=4634.
So odd one out is 914.
35. Let the son’s present age be x years.
Then, (38-x) = x
 2x = 38
x = 19
∴ Son’s age 5 years back (19-5) = 14 years
46. Each second number is the half of first
number.
So, 125 is the half of 250.
36. By I & II, we can get Priya’s age.
So, Both I & II
37. Ans is 312
The last digit’s we ‘2’ & the first digits are
twice themselves & adding one.
38. Ans is 248
Each number is twice the before number &
Adding 0, 1, 2, 3, …..to it.
39. Ans is 558
The first two numbers are multiples of 11 &
the third number is in the order of 5, 6, 7, 8,
9, 10.
40. The ‘13’ is the next number, The next prime
number is ‘17’ So, ans is 13, 17
41. Ans is 101
Consecutive numbers
Taking two at a time
11-1 = 10
1001-1 = 1000
So in the blank 101-1 = 100
42. All the question types has square of 2, 3, 4, 5,
6, 7,…. So, the ans is 3649
43. The addition of first two numbers gives the
third number. Likewise, 67+79 = 146
44. The addition of all numbers gives the sum of
11 except 4443 which gives the addition of
15 So, the ans is 4443
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36 HOUR PLACEMENT CLASS SHEET
QUANTITATIVE APPTITUDE
8
ANSWER KEY
1)
b
2)
d
3)
b
4)
a
5)
b
6)
c
7)
b
8)
d
9)
d
10)
c
11)
b
12)
c
13)
d
14)
d
15)
c
16)
a
17)
b
18)
d
19)
a
20)
d
21)
b
22)
d
23)
c
24)
c
25)
a
26)
d
27)
d
28)
a
29)
d
30)
a
31)
a
32)
c
33)
c
34)
a
35)
a
36)
e
37)
a
38)
c
39)
c
40)
c
41)
a
42)
b
43)
d
44)
a
45)
d
46)
c
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