Mathematics · Quantitative Aptitude
Number Sums and Series
268 Questions
Number sums and series questions test the ability to find patterns and calculate the sum of number sequences. These problems are a staple in the quantitative aptitude sections of various competitive exams. Practice this collection to improve speed and accuracy in solving arithmetic and geometric series problems.
Sum of consecutive integersGeometric series sumsRatio and proportion sumsOdd and even number propertiesRoman numeral calculations
Number Sums and Series Questions
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3 and 1
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16 and 4
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4 and 5
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1 and 3
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9 and 8
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4 and 12
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16 and 2
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8 and 4
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9 and 3
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4 and 7
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11 and 2
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None of these
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20
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30
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40
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50
-
None of these
A
Correct answer
Explanation
Let the numbers be a, b and c.
Then, a2 + b2 + c2 = 138 and (ab + bc + ca) = 131
(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca) = 138 + 2 x 131 = 400
(a + b + c) = 20
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104
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114
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315
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325
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None of these
B
Correct answer
Explanation
Let the numbers be x and y.
Then, x + y = 25 and x - y = 13.
4xy = (x + y)2 - (x- y)2
4xy = (25)2 - (13)2
4xy = (625 - 169) = 456
xy = 114
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34
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38
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42
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46
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None of these
C
Correct answer
Explanation
This is the correct answer.
Let the numbers be x and x + 2.
Then, (x + 2)
2 - x
2 = 84
4x + 4 = 84
4x = 80
x = 20
The required sum = x + (x + 2) = 2x + 2 = 42
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380
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395
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400
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425
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None of these
C
Correct answer
Explanation
Let the numbers be x and y.
Then, xy = 9375 and x/y = 15
(xy)/(x/y) = 9375/15
y2 = 625
y = 25
x = 15y
= (15 x 25) = 375
Sum of the numbers = x + y = 375 + 25 = 400.
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20
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23
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169
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170
-
None of these
B
Correct answer
Explanation
This is the correct answer.
Let the numbers be x and y.
Then, xy = 120 and x
2 + y
2 = 289.
(x + y)
2 = x
2 + y
2 + 2xy
= 289 + (2 x 120)
= 529
x + y = 23
C
Correct answer
Explanation
1456 + 2400 = 3856
4000 is nearest to 3856 as compared to 3000.
A
Correct answer
Explanation
1156 + 4444 = 5600
6000 is nearest to 5600 as compared to 5000.
C
Correct answer
Explanation
Let GP be a/r, a, ar. Sum: a/r + a + ar = 38. Product: a^3 = 1728, so a = 12. With a=12, testing r=3/2 gives: 8, 12, 18. Sum = 38, product = 1728. Smallest term is 8.
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4, 6, 9
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3, 7, 9
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11, 6, 2
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None of these
A
Correct answer
Explanation
For three numbers in G.P, let them be a/r, a, ar. Sum = a/r + a + ar = 19. Product = (a/r) x a x ar = a³ = 216, so a = 6. Substituting: 6/r + 6 + 6r = 19. Divide by 6: 1/r + 1 + r = 19/6. Multiply by r: 1 + r + r² = 19r/6. This gives r = 1.5 or 2/3. So numbers are 4, 6, 9 (with r = 1.5) or 9, 6, 4 (with r = 2/3). Option A matches one valid ordering.
B
Correct answer
Explanation
This is an infinite geometric series with first term a = 1 and common ratio r = 2/3. The sum of an infinite GP is S = a/(1-r) when |r| < 1. Here, S = 1/(1 - 2/3) = 1/(1/3) = 3. The series converges because 2/3 < 1.
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12, 18, 40
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10, 20, 40
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40, 20, 10
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None of these
B
Correct answer
Explanation
Let the three numbers in G.P. be a/r, a, ar. Their sum is 70. When extremes are multiplied by 4 and mean by 5, we get 4a/r, 5a, 4ar. For these to be in A.P., the middle term must equal the average of first and third: 5a = (4a/r + 4ar)/2. Solving with sum=70 gives the numbers 10, 20, 40. Check: 10+20+40=70 and 4×10, 5×20, 4×40 = 40, 100, 160 which is an A.P. with common difference 60.
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5, 7, 9
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9, 5, 7
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7, 5, 9
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None of these
A
Correct answer
Explanation
Let the AP be (a-d), a, (a+d). Sum = 3a = 21, so a = 7. After adding 1, 5, 15 respectively: (8-d), 12, (22+d). For GP: 12^2 = (8-d)(22+d). Solving d^2 + 14d - 32 = 0 gives d = 2 or d = -16. For d = 2: numbers are 5, 7, 9. For d = -16: numbers are 23, 7, -9. Both work, but only 5, 7, 9 appears in the options.