Number Series Reasoning Questions (Aptitude), Test Your Reasoning Ability

Ques 1: 9587-? = 7429-4358

• 6516
• 7421
• 6561
• 6428

6516
Sol. Let 9587-x = 7429-4358. Then,
9587-x = 3071
x = 9587-3071 = 6516

Ques 2: 5793405×9999 = ?

• 57928256586
• 65928256545
• 75928256595
• 57928256595

57928256595
Sol. = 5793405x(10000-1)
= 57934050000-5793405
= 57928256595

Ques 3: 839478×625 = ?

• 524673710
• 524673750
• 534673750
• 598673750

524673750
Sol. 839478 x 5⁴
= 8394780000/16
= 524673750

Ques 4: 976×237+976×763 = ?

• 824000
• 769000
• 976000
• 912000

976000
Sol. Using distributive law, we get :
= 976×237+976+763 = 976x(237+763)
= 976×1000
=976000

Ques 5: 986×307-986×207 = ?

• 72600
• 98600
• 98621
• 45870

98600
Sol. By using distributive law, we get
= 986×307-986×207 = 986x(307-207)
= 986×100
= 98600

Ques 6: 1607×1607 =?

• 3582789
• 2582449
• 4587659
• 6548449

2582449
Sol. 1607 x 1607
= 1607²
= (1600+7)²
= 16002 + 7² + 2 x 1600 x 7
= 2560000 + 49 +22400
= 2582449

Ques 7: 1396×1396 = ?

• 1848946
• 1547966
• 1948816
• 1948836

1948816
Sol. 1396 x 1396
= 1396²
= (1400-4)²
= 1400² + 4² – 2 x 1400 x 4
= 1960000 + 16 – 11200
= 1948816

Ques 8: (475×475+125×125) = ?

• 356450
• 241250
• 124550
• 521250

241250
Sol.We have (a² + b²) =
1/2 [(a + b)² + (a – b)²]
=(475)² + (125)² =
1/2 [(475 + 125)² + (475 – 125)²]
= 1/2 [360000 + 122500]
= 241250

Ques 9: (796×796-204×204) = ?

• 632000
• 592000
• 548700
• 658900

592000
Sol. 796×796-204×204
=(796)²−(204)²
= (796+204)(796-204)
= 1000×592
= 592000

Ques 10: (387×387+113×113+2x387x113) = ?

• 245600
• 458700
• 250000
• 256400

250000
Sol. 387×387+114×114+2×387×114
= (387)²+(113)² + 2×387×113
= (387+113)²
[ Since , (a+b)²=a²+b²+2ab]
= 500²
=250000

Ques 11: (87×87+61×61-2x87x61) = ?

• 476
• 676
• 872
• 576

676
Sol. (87)²+(61)²-2x87x61

(a²+b²−2ab) where a = 87 and b = 61.
=(a−b)²=(87−61)²
=(26)²
=(20+6)²
=(20)²+(6)²+2x20x6
= 400 + 36 + 240)
= 676

Ques 12: Find the least value of * for which 5967*13 is divisible by 3.

• 2
• 1
• 5
• 10

2
Sol. Let the required value be x. Then,
(5+9+6+7+x+1+3 = (x+31) is divible by 3
Least value of x is 2

Ques 13: Find the least value of * for which 7*5462 is divisible by 9.

• 4
• 9
• 8
• 3

3
Sol. Let the required value of x . Then
(7+x+5+4+6+2)=(24+x) is divisible by 9
Least value of * is 3

Ques 14: Find the least value of * for which 4832*18 is divisible by 11.

• 5
• 11
• 7
• 4

7
Sol. (Sum of digits at odd places) – (Sum of digits at even places)
= (8+x+3+4) – (1+2+8)
= (4+x), which should be divisible by 11
x = 7

Ques 15: What least number must be subtracted from 1672 to obtain a number which is completely divisible by 17?

• 6
• 5
• 4
• 7

6
Sol. When 1672 is divided by 17, then 6 is the reminder.
Hence, 6 must be subtracted.

Ques 16: What is the least number to be added to 2010 to obtain a number which is completely divisible by 19?

• 5
• 9
• 4
• 7

4
Sol. When 2010 is divided by 19, 15 is the reminder.
So, 19-15 = 4
Hence, 4 must be added.

Ques 17: On dividing 12401 by a certain number, we get 76 as quotient and 13 as reminder. What is the divisor?

• 173
• 185
• 163
• 142

163
Sol. Dividend = Divisor × Quotient + Remainder
12401 = 76*N + 13
N = (12401 – 13)/76
= 12388/76
= 3097/19
= 163

Ques 18: On dividing a certain number by 342, we get 47 as remainder. If the same number is divided by 18, what will be the remainder?

• 21
• 13
• 10
• 11

11
Sol. Suppose that on dividing the given number by 342, we get quotient = k and remainder = 47. Then,
Number = 342k + 47
= (18x19k) + (18×2) = 11
=18x(19k+2)+11
So, the number when divided by 18 gives remainder = 11.

Ques 19: Simplify : (789x789x789 + 211x211x211)/(789×789-789×211+211×211) =?

• 1500
• 500
• 100
• 1000

1000
Sol. Given exp. = ((789)³+(211)³)/(789)²-(789×211)+(211)²)
= (a³+b³)/(a²-ab+b²), where a = 789 and b = 211
=(a+b) = (789+211) = 1000

Ques 20: Simplify : (658x658x658 – 328x328x328)/(658×658+658×328+328×328) =?

• 315
• 330
• 320
• 350

330
Sol. Given exp. = ((658)³-(328)³)/(658)²+(658×328)+(328)²)
= (a³-b³)/(a²+ab+b²), where a = 658 and b = 328
=(a-b) = (658-328) = 330

Ques 21: Simplify :
((893+786)²-(893-786)²)/(893×786)

• 8
• 5
• 4
• 3

4
Sol. Given exp. = ((a+b)²-(a-b)²)/ab, where a = 893 and b = 786
= 4ab/ab
= 4

Ques 22: What is the unit digit in the product (684x759x413x676)?

• 4
• 8
• 10
• 9

8
Sol. Unit digit in the given product
= Unit digit in the product (4x9x3x6) = 8

Ques 23: What is the unit digit in the product {(3547)¹⁵³x(251)⁷²}?

• 7
• 5
• 4
• 9

7
Sol. Required digit = unit digit in (7¹⁵³x1⁷²)
Now, 7⁴ gives unit digit 1 and 1⁷² = 1
(7¹⁵³x1⁷²) = [(7⁴)³⁸x7x1] = 7
Required unit digit = (1x7x1) = 7

Ques 24: What is the unit digit in {(264)¹⁰²+(264)¹⁰³}?

• 0
• 1
• 7
• 5

0
Sol. (264)¹⁰²+(264)¹⁰³ = (264)¹⁰²{1+264} = (264)¹⁰²x265
Required unit digit = unit digit in [(4)¹⁰²x5]
=unit digit in [(4⁴)²⁵x4²x5]
=unit digit in (6x6x5) = 0

Ques 25: Find the total number of prime factors in the product {(4)¹¹x7⁵x(11)²}

• 29
• 20
• 16
• 10

29
Sol. (4)¹¹ x (7)⁵ x (11)²
= (2 x 2)¹¹ x (7)⁵ x (11)²
= 2¹¹ x 2¹¹ x 7⁵ x 11²
= 2²² x 7⁵ x 11²
Total number of prime factors = (22 + 5 + 2) = 29