Quantitative Questions on Numbers pt. 1

Quantitative Questions on Numbers

Quantitative Questions on Numbers pt. 1

Q1. The sum of three consecutive numbers is 93. The greatest among these three numbers is

একেৰাহে তিনিটা সংখ্যাৰ যোগফল হৈছে 93, এই তিনিটা সংখ্যাৰ ভিতৰত আটাইতকৈ ডাঙৰ টো হ’ল

(a) 27
(b) 28
(c) 30
(d) 32

Answer: (d) 32

Let the three numbers are x, x+1 and x+2

Then x+(x+1)+(x+2)=93

3x=90

x=30

Greater Number=(x+2)=32

 

Q2. The sum of four consecutive even integers is 1092. The greatest of them is

একেৰাহে চাৰিটা আনকি পূৰ্ণসংখ্যাৰ যোগফল হৈছে ১০৯২, এইকেইটাৰ ভিতৰত আটাইতকৈ ডাঙৰ টো হ’ল

(a) 270
(b) 300
(c) 276
(d) 302

Answer: (c) 276

Let the four integers be x, x+2, x+4 and x+6

Then x+(x+2)+(x+4)+(x+6)=1092

4x=1080

x=270

Greater Number=(x+6)=276

 

Q3. The sum of three consecutive odd numbers is 10 more then the first of these numbers. What is the greatest number

একেৰাহে তিনিটা অদ্ভূত সংখ্যাৰ যোগফল হৈছে 10 টা অধিক তাৰ পিছত এই সংখ্যাবোৰৰ প্ৰথমটো। আটাইতকৈ ডাঙৰ সংখ্যা টো কি

(a) 6
(b) 8
(c) 9
(d) 12

Answer: (a) 6

Let the four integers be x, x+2 and x+4

Then x+(x+2)+(x+4)=x+10

2x=4

x=2

So the Greatest Number is=(2+4)=6

 

Q4. The difference of the squares of two consecutive odd numbers is 84. What is the sum of the two numbers

একেৰাহে দুটা অদ্ভূত সংখ্যাৰ বৰ্গৰ পাৰ্থক্য হৈছে ৮৪, সংখ্যা দুটাৰ যোগফল কিমান

(a) 40
(b) 42
(c) 45
(d) 48

Answer: (b) 42

Let the two numbers is x and x+2

Then (x+2)2 – x2=84

4x+4=84

x=20

Required Sum is=x+(x+2)=42

 

Q5. The difference between two numbers is 5 and their sum is 65. What will be their product

দুটা সংখ্যাৰ মাজৰ পাৰ্থক্য হৈছে 5 আৰু সেইবোৰৰ যোগফল হৈছে 65। তেওঁলোকৰ সামগ্ৰী কি হ’ব

(a) 325
(b) 650
(c) 755
(d) 1050

Answer: (d) 1050

Let the two numbers is X and Y

X-Y=5

X+Y=65

2X=70

X=35, so Y is 30

So X*Y = 1050

 

Q6. 759 X 568 + 759 X 432 = ?

(a) 756800
(b) 759000
(c) 568000
(d) 432000

Answer: (b) 759000

=759 X 568 + 759 X 432

=759 (568 + 432)

=759 X 1000

=759000

 

Q7. 832 X 455 – 832 X 355 = ?

(a) 83200
(b) 82300
(c) 8320
(d) 832000

Answer: (a) 83200

=832 X 455 – 832 X 355

=832 (455 – 355)

=832 X 100

=83200

 

Q8. 105 X 105

(a) 10500
(b) 11250
(c) 11520
(d) 11025

Answer: (d) 11025

=105 X 105

=(105)2

=(100 + 5)2

=1002 + (2 X 100 X 5) + 52  Formula [(a+b)2=a2+2ab+b2]

=10000 + 1000 + 25

=11025

 

Q9. 96 X 96

(a) 9216
(b) 9261
(c) 9006
(d) 9466

Answer: (a) 9216

=96 X 96

=(96)2

=(100 – 4)2

=1002 – (2 X 100 X 4) + 42  Formula [(a-b)2=a2-2ab+b2]

=10000 – 800 + 16

=9200 + 16

=9216

 

Q10. 456 X 456 – 302 X 302

(a) 128734
(b) 118564
(c) 116732
(d) 127856

Answer: (c) 116732

=456 X 456 – 302 X 302

=(456)2 – (302)2

=(456+302) – (456-302)  Formula [a2 – b2=(a+b)(a-b)]

=758 X 154

=116732

 

Q11. 86 X 86 – 14 X 14

(a) 7020
(b) 7156
(c) 7200
(d) 7400

Answer: (c) 7200

=86 X 86 – 14 X 14

=(86)2 – (14)2

=(86+14) – (86-14)  Formula [a2 – b2=(a+b)(a-b)]

=100 X 72

=7200

 

Q12.

(251 X 251 X 251) – (69 X 69 X 69)
(251 X 251 + 251 X 69 + 69 X 69)

(a) 180
(b) 182
(c) 285
(d) 1081

Answer: (b) 182

=

(251 X 251 X 251) – (69 X 69 X 69)
(251 X 251 + 251 X 69 + 69 X 69)

=

(251)3 – (69)3
(251)2 + (251 X 69) + (69)2

=

(251 – 69) (2512 + 251 X 69 + 692)
(2512 + 251 X 69 + 692)

=251 – 69

=182

Formula a3 – b3=(a-b)(a2+ab+b2)

 

Q13.

(407 + 315)2 – (407 – 315)2
407 X 315

 

(a) 41
(b) 401
(c) 4
(d) 104

Answer: (c) 4

=

(407 + 315)2 – (407 – 315)2
407 X 315

=

4 X 407 X 315
407 X 315

=4

Formula (a+b)2 – (a-b)2 = 4ab

 

Q14.

(215 + 102)2 + (215 – 102)2
215 X 215 + 102 X 102

(a) 2
(b) 12
(c) 102
(d) 215

Answer: (a) 2

=

(215 + 102)2 + (215 – 102)2
215 X 215 + 102 X 102

=

2(2152 + 1022)
2152 + 1022

=2

 

Q15. 1 + 2 + 3 + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + 20 = ?

(a) 20
(b) 120
(c) 201
(d) 210

Answer: (d) 210

=1 + 2 + 3 + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + 20

=20 (20 + 1) ÷ 2

=10 X 21

=210

Formula 1 + 2 + 3 + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + n = n(n + 1) ÷ 2

 

Q16. 3 + 4 + 5 + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + 20 = ?

(a) 205
(b) 206
(c) 207
(d) 208

Answer: (c) 207

=3 + 4 + 5 + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + 20

=1 + 2 + 3 + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + 20 – (1 + 2)

=[20 (20 + 1) ÷ 2] – 3

=10 X 21 – 3

=210 -3

=207

Formula 1 + 2 + 3 + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + n = n(n + 1) ÷ 2

 

Q17. 12 + 22 + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + 102 = ?

(a) 285
(b) 385
(c) 485
(d) 585

Answer: (b) 385

=12 + 22 + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + 102

=[10 (10 + 1) (2 X 10 + 1)] ÷ 6

=(10 X 11 X 21) ÷ 6

=385

Formula 12 + 22 + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + n2 = [n(n+1)(2n+1) ÷ 6

 

Q18. 32 + 42 + 52 + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + 102 = ?

(a) 380
(b) 382
(c) 384
(d) 386

Answer: (a) 380

=32 + 42 + 52 + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + 102

=12 + 22 + 32 + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + 102 – (12 + 22)

=[10 (10 + 1) (2 X 10 + 1) ÷ 6] – (1+4)

=[10 X 11 X 21 ÷ 6] – 5

=385 – 5

=380

 

Q19. 13 + 23 + 33 + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + 103 = ?

(a) 2025
(b) 3025
(c) 3052
(d) 3205

Answer: (b) 3025

=13 + 23 + 33 + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + 103

=

102(10 + 1)2
4

=

100 X 121
4

=3025

Formula [13 + 23 + ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ + n3] =[n2(n + 1)2] ÷ 4

 

Q20. The difference between the place value and face value of 5 in the number 835422 is

835422 নম্বৰত স্থানমূল্য আৰু মুখমূল্য 5 ৰ মাজৰ পাৰ্থক্য হৈছে

(a) 4995
(b) 5000
(c) 5005
(d) 5995

Answer: (a) 4995

Place value of 5 = 5000

Face value of 5 = 5

Diference = 4995

 

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