Operations

In Rajshahi 5 adults are unemployed for every 120 adults who

have jobs. Out of 2125 adults, how many have jobs?
(A) 89 (B) 425 (C) 2040 (D) 1896 (E) None of these

Ans: (C)
 Jubair has Tk. 1.80,000 in his bank account. He made the
following transactions: checksWere written for Tk 20,000, Tk 13,000, Tk
40,000 and Tk 18,000 . Deposits of Tk 60,000 and Tk 103,000 were made in the
account. Interest amount added in the balance was Tk 50,000 and service fees
charged by the bank was Tk 15,000 . What is the final balance to the account?
(A)Tk 45,000 (B) Tk 285,000 (C) Tk 215,000 (D) Tk 185,000 (E) None of these
Ans: (E)
 If a typist can type 125 pages, 36 lines each, 11 words to each
line in 5 day, how many pages of 30 lines each and 12 words to each line can he
type in 6 days?
(A) 180 (B) 175 (C) 170 (D) 165 (E) none of these
Ans: (D)
 If 4 is subtracted from one-fourth of a number, the result is 20.
The number is -
(A) 84 (B) 92 (C) 108 (D) 116 (E) none of these

Ans: (E)
 If CAC multiplied by DD equals to DDDD and if D=7, then what
is the value of A ?
(A) 7 (B) 6 (C) 0 (D) 2 (E) none of these
Ans: (C)
 If an electric typewriter prints one word per second, what is the
approximate time required for this typewriter to print a million words?
(A) 10 hours (B) 10 days (C) 10 weeks (D) 10 months (E) 10 years

Ans: (B)
 What is the total number of integers between 100 and 200 that are
divisible by 3?
(A) 33 (B) 32 (C) 31 (D) 30 (E) one of these

Ans: (A)
 A number when divided by a divisor leaves a remainder of 24.
When twice the original number is divided by the same divisor the remainder is
11 . What is the value of the divisor?
(A) 13 (B) 59 (C) 35 (D) 37 (E) 12
Ans: (D)
 When positive integer x is divided by positive integer y, the
remainder is 9. If x/y = 96.12, what is the value of y?
(A) 96 (B) 75 (C) 48 (D) 25 (E) 12

Ans: (B)
 How many prime numbers are there between 56 and 100?
(A) 8 (B) 9 (C) 10 (D) 11 (E) none of these

Ans: (B)
 If x and Y are two distinct positive integers divisible by 4, then
which of the following is necessarily divisible by 8?
(A) x + y (B) x - y (C) 𝑥 2 + 𝑦 2 (D) 2x + y (E) none of these
Ans: (C)
 What is the smallest number of apples that can be distributed
equally among 4, 6, 9 or 15 students having a surplus of two apples each time?
(A) 422 (B) 362 (C) 182 (D) 62 (E) none of these
Ans: (C)
 441 + 442 + 443 is divisible by –
(A) 7 (B) 13 (C) 15 (D) 17 (E) none of these
Ans: (A)
 The difference between two hundred nine thousand fourteen and
ninety three thousand seven hundred nine is –
(A) 116,315 (B) 115,315 (C) 116,305 (D) 115,305 (E) None of these

Ans: (D) The difference between two hundred nine

thousand fourteen and ninety three thousand
seven hundred nine is. 209014- 93709 = 115305
সু তর াং (D) সঠিক answer.
 A club collected exactly Tk 599 from its members. If each
member contributed at least Tk 12, what is the greatest number of members the
club could have?
(A) 48 (B) 49 (C) 50 (D) 51 (E) none of these
Ans: (B) ম ট 599 ট ক collected হয়েয়ে এবাং minimum
contribution 12 ট ক হয়ে সম্ভ বয সয়বব চ্চ মে য়কর সাংখ্য =
49 ক রণ 49 × 12 = 588 ঠকন্তু 50 × 12 = 600, য সী র
অঠতঠরক্ত। সু তর াং (B) সঠিক answer.
 If the product of 3 consecutive integers is 120, then the sum of
the integers is -
(A) 9 (B) 12 (C) 14 (D) 15 (E) 18

Ans: (D) 120 এর উৎপ দকগুয়ে হয়ে 1, 2, 3, 4, 5, 6 ইতয ঠদ।

4, 5 ও 6 মক গুণ করয়ে 120 হে। 4 + 5 + 6 = 15
 3 and 5 are factors of F. From this information, we can conclude
that –
(A) 8 is a factor of F (B) F is a multiple of 15 (C) F = 3 x 5
(D) 15 is a multiple of 15 (E) 3 and 5 are the only factors of F

Ans: (B) Given that 3 and 5 are factors of F.

Since 3 and 5 are not the only factors of F, F = 3 x 5 x (other factors)
Or, F = 15 x (other factors)
Therefore, F could be any multiple of 15.
 If the product of (1+2),(2-3) and (3+4) is equal to half the sum of
20 and x, then x =?
(A) 210 (B) 190 (C ) 105 (D) 85 (E) 10
20+𝑥
Ans: (B) 1 + 2 2 + 3 3 + 4 =
2
⇒ 105 × 2 = 20 + 𝑥 ⇒ 210 − 20 = 𝑥 ⇒ 𝑥 = 190
 A man invested in a life insurance policy. He paid the insurance
company an annual premium of Tk. 20 for insurance of every thousand taka.
His insurance was for Tk. 4,500. The man died after making 27 annual
installments. Total sum paid by the insurance company was Tk. 7,800. By how
much did the sum paid by the insurance company exceed the total amount of
premium that the man paid to the insurance company?
(A) 5370 (B) 4750 (C) 4500 (D) 3300 (E) none of these
Ans: (A) 1000 ট ক ে premium 20 ট ক
∴ 4500 ট ক ে premium ((20 x 4500)/1000) = 90 ট ক
∴ 27 বেয়রর প্রদত্ত premimum = 90 x 27 = 2430 ট ক
উত্তর = 7800 – 2430 = 5370 ট ক
 Which of the following is the product of two positive integers
whose sum is 3?
(A) 0 (B) 1 (C) 2 (D) 3 (E) 4
Ans: (C) দুঠট ধন ত্মক পূণবসাংখ্য র ময গফে 3 অর্ব ৎ
সাংখ্য দ্বে 2 ও 1। অতএব, ত য়দর গুণফে = 2 x 1 = 2
 How many positive integers less than 20 are equal to the sum of a
positive multiple of 3 and a positive multiple of 4?
(A) Eleven (B) Five (C) Seven (D) Ten (E) none of these

Ans: (D) 20 এর মেয়ে মে ট positive multiples of 3 = 3, 6, 9, 12, 15, 18

20 এর মেয়ে মে ট p, ositive multiples of 4 = 4, 8, 12, 16
ময গ করয়ে মদখ্ য ে, 3 + 4 = 7, 3 + 8 = 11, 3 + 12 = 15, 3 + 16 = 19
6 + 4 = 10, 6 + 8 = 14, 6 + 12 = 18
9 + 4 = 13, 9 + 8 = 17
12 + 4 = 16
15 + 4 =19
ম ট positive integer = 7, 10, 11, 13, 14, 15, 16, 17, 18, 19 = 10 ঠট
 Janata Garments Ltd. (JGL) has specific sales targets for all its
sales managers. One of the managers Mr. Dhiman has a sales target of taka 50
million per quarter. Accounts show that during the first three quarters he has
sold taka 10, 15, and 20 million worth of goods respectively. How much in taka
should Mr. Dhiman sell during the fourth quarter in order to maintain the
average sales target?
A) 10 million B) 5 million C) 250 million D) 155 million E) None of these

Ans: (D) The target is 50 Million per quarter, or the

average of the sum of all of the quarters will be 50
Million. Let, the sales of 4th quarter be x millions.
(10 + 15 + 20 + X)/4 = 50
Or, x = 155
 If x/y = 3/7, then which of the following cannot be a
possible value of (y - x)?
(A) 4 (B) 21 (C) 24 (D) 84 (E) None of these

Ans: (E) x এবাং y যঠদ integer হত, ত হয়ে y – x এর value 7 – 3 ব

4 এর multiple হত।
ঠকন্তু এখ্ য়ন x এবাং y integer ঠকন ত উয়েখ্ কর মনই।
ক য়েই প্রদত্ত options A, B, C, D এর মযয়ক নঠটই y – x এর value
হয়ত প য়র।
 What is the greatest positive integer n such that 2n is a factor of
1210? (A) 10 (B) 12 (C) 16 (D) 20 (E) 60

Ans: (D) 1210 = 310 x 410 = 310 x (22)10 = 310 x 220

 Find the smallest number which when divided by 18 and 24 will
have a remainder of 4 and 10 respectively?
(A) 56 (B) 52 (C) 58 (D) 54 (E) none of these

Ans: (C) 19 আর 24 এর ে.স .গু = 72 আব র 18 – 4 = 14 এবাং

24 – 10 = 14, এখ্ন 72 – 14 = 58 হয়ব smallest number
 If # is an operator such that (4 #2 = 14) and (2 #3 = 6) what will be
the value of (5 # 2)?
(A) 11 (B) 19 (C) 23 (D) 25 (E) none of these.

Ans: (C) Here the system is such that a#b = (a)b - 2

So 4#2 = (4)2 - 2 = 14, and 2#3 =(2)3 - 2 = 6
Therefore, 5#2 = (5)2 - 2 = 23
 If (a + a + a) = ( b + b + b + b) and (a+ b) = 7, then what is the
value of (a2 – b2)?
(A) 0 (B) 3 (C) 4 (D) 7 (E) none of these

Ans: (D) 3a = 4b এবাং a + b =7 মর্য়ক প ই a = 4, b = 3

অতএব, (a2 – b2) = 16 – 9 = 7
 How many prime numbers are there between 1 and 10?
(A) 2 (B) 3 (C) 4 (D) 5 (E) 6

Ans: (C) 1 and 10 এর ঠিতর prime number হয়ে 2, 3, 5, 7;

অতএব, ে রট ম ৌঠেক সাংখ্য
 How many integers between 110 and 120 are prime numbers?
(A) 0 (B) 1 (C) 2 (D) 3 (E) 4

Ans: (B) The only prime number between 110 and 120 is 113.
 If y /3, y / 4 and y /7 represent integers, then y can be –
(A) 42 (B) 56 (C) 70 (D) 84 (E) 126

Ans: (D) y হয়ব এ ন একঠট সাংখ্য য 3, 4, 7 দ্ব র ঠবি েয। ময ন, 84

সু তর াং, (D) সঠিক Answer.
 If n is an integer divisible by 6 but not by 4, then which of the
following CANNOT be an integer?
( A) n/2 (B) n/3 (C) n/6 (D) n/10 (E) n/ 12
Ans: (E) n, 6 দ্ব র ঠবি েয ঠকন্তু 4 দ্ব র নে ময ন, 18, 30,
42 ইতয ঠদ n এর ন হয়ত প য়র। এর মযয়হতু মে ড় সাংখ্য
এবাং 6 দ্ব র ঠবি েয ত ই 2, 3, 6 দ্ব র ও ঠবি েয হয়ব। 30, 10
দ্ব র ঠবি েয। ঠকন্তু এর কখ্নই ঠবি েয হয়ব ন ।
 180 students in a group are to be seated in rows so that there are
an equal number of students in each row. Each of the following could be the
number of rows EXCEPT -
(A) 4 (B) 20 (C) 30 (D) 40 (E) 90
Ans: (D) এই মেয়ে, number of rows মক 180 এর factor হয়ত হয়ব
মযয়হতু প্রয়তযক row মত স ন সাংখ্যক students বয়স। মযয়হতু 40, 180 এর
factor ন , এখ্ য়ন 40 ট row র্ কয়ত প রয়বন। সু তর াং (D) সঠিক answer.
 What is the minimum number of chocolates that must be added to
the existing stock of 270 chocolates so that the total stock can equally be
divided among 6, 8 or 12 persons?
(A) 12 (B) 16 (C) 18 (D) 20 (E) none of these

Ans: (C) 6, 8 এবাং 12 এর ে. স . গু = 24

অর্ব ৎ, ম ট no of chocolates হয়ব 24 এর গুঠণতক।
270 এর মর্য়ক minimum উপয়র 24 এর গুঠণতক = 288
অর্ব ৎ, add করয়ত হয়ব (288-270) = 18 ঠট
 One third, one fourth, one fifth and one-seventh of the human
population of Island X, which has fewer than 5000 human inhabitants, are all
whole numbers and their sum is exactly the population of Island Y. What is the
population of Island Y?
(A) 4200 (B) 4279 (C) 4581 (D) 4800 (E) Cannot be determined

Ans: (E) 3, 4, 5 ও 7 এর ে.স .গু. মবর করয়ত হয়ব। ে.স .গু = 420
বে হয়েয়ে Island x এর েনসাংখ্য 5000 এর ক । এখ্ন x এর েনসাংখ্য
4279 হে (Answer choice B) সু তর াং, answer হওে উঠেৎ cannot be
determined.
 The greatest common fact or of two positive integers is A. The
least common multiple of the two integers is B. If one of the integers is C, what
is the other number?
(A ) AB/C (B) BC/A (C)A/C + B (D) A + B/C (E) none of these

Ans: (A) Let, the number be x.

The product of two numbers is equal to the product of the
HCF and LCM of the two numbers.
Therefore, xC = AB
Or, x=AB/C
 If y is an integer divisible by 3 but not by 2 then which of the
following will never be an integer?
𝑦−1 7 𝑦 𝑦3
(A) (B) (C) (D) (E) none of these
2 7 24 3

Ans: (C) y মযয়হতু 2 ঠদয়ে ঠবি েয নে, ত ই মক ন মে ড়

সাংখ্য ঠদয়ে y মক ি গ কর য য়ব ন ।
 Mr. Saif has n luxury apartments, where n is an integer such that
20 < n < 50. If he divides the apartments equally among his 5 children, he will
have 2 apartments remaining. If he divides the apartments among 6 children, he
will have 1 apartment remaining. How many apartments will remain if he
divides the apartments among 7 children?
(A) 3 (B) 2 (C) 4 (D) 1 (E) none of these

Ans: (B) Mr. Saif এর apartment এর সাংখ্য 20 < n < 50

যখ্ন ঠতঠন apartments 5 েন এর য়ধয ি গ কয়র মদন, ব ঠক র্ য়ক 2 ঠট apartment.
সু তর াং, 20 মর্য়ক 50 এর য়ধয 5 ঠদয়ে ি গ করয়ে 2 ি গয়েষ র্ য়ক এ ন সাংখ্য আয়ে 22, 27, 32,
37, 42 এবাং 47
যখ্ন ঠতঠন apartments 7 েন এর য়ধয ি গ কয়র মদন, ব ঠক র্ য়ক 1 ঠট apartment.
সু তর াং, উপযুবক্ত সাংখ্য গুয়ে র য়ধয 6 ঠদয়ে ি গ করয়ে 1 ি গয়েষ র্ য়ক এ ন সাংখ্য আয়ে শুধু ে 37।
37 ঠট apartment 7 েন এর য়ধয ি গ করয়ে ব ঠক র্ কয়ব 2 ঠট।
 When x is divided by 13, the answer is y with a remainder of 3.
When x is divided by 7, the answer is z with a remainder of 3. If x, y, and z are
all possible integers, what is the remainder of yz/13? (3,4,5)
(A) 0 (B) 3 (C ) 4 (D) 7 (E) none of these

Ans: (A) For 1st case, x= l3y+3 ......... (i)

For 2nd case, x= 7z+3 ............ (ii)
From (i) and (ii), 13y + 3 = 7z + 3
⇒ 13y = 7z
As 7 and 13 both are prime numbers, the only possible value for y and z would be
7 and 13 (If one of them is 7, other would be 13).
So, yz/13= 7.13/13 = 7 (No remainder)