Mathematics Questions and Answers – Patterns in Squares of Numbers

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This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Patterns in Squares of Numbers”.

1. What kind of figure does the number 15 show in triangular representation?
a) Triangular form with base 5
b) Triangular form with base 4
c) Triangular form with base 3
d) Triangular form with peak 1
View Answer

Answer: a
Explanation: Triangular numbers are the numbers which form a triangle when arranged in increasing form. When the number 15 is arranged in increasing form the base of the triangle has 5 dots, which goes on decreasing and reaches the peak upto 1.
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2. When we add fourth and fifth triangular number we get ______
a) 52
b) 62
c) 252
d) 253
View Answer

Answer: a
Explanation: The fourth and fifth triangular numbers are 10 & 15.
10 + 15 = 25 = 52. Therefore 52 is the correct answer and the other options are incorrect. The options should be read carefully as the options are very close.

3. There are _____ non-square numbers between 652 & 662.
a) 130
b) 65
c) 131
d) 129
View Answer

Answer: c
Explanation: In these types of questions we can use the shortcut in order to reach the answer quickly. We can use the formula (2n+1). When we use this formula we consider one of the numbers as n and the hence the second number is(n+1). Here n=65.
Therefore when we substitute n=65 in the formula we get,
[2×(65)+1]=131.
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4. In some cases, there can be less than two non-square numbers between two square numbers.
a) True
b) False
View Answer

Answer: a
Explanation: There are two cases where there are less than two non-square numbers between two square numbers, the cases are as follows.
Case 1:- 02 & 12 Here there is not a single number between squares.
Case 2:- 12 & 22 Here there are two numbers between the squares.
Hence the given statement is true and cannot be false.

5. We get the square of _____ number if we add first 11 odd numbers.
a) 11
b) 12
c) 5
d) 13
View Answer

Answer: a
Explanation: There is an interesting pattern in squares, when we add first n odd numbers we get n2. So here when we add the first eleven odd numbers, we get 112. Hence the correct answer would be 112 and the other options would be incorrect.
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6. On subtracting first 25 odd numbers from first 30 odd numbers we get _____
a) 52
b) 375
c) 5
d) 275
View Answer

Answer: c
Explanation: If we add the first 25 odd numbers, we get 625 (i.e.252) and when we add first 30 odd numbers, we get 900 (i.e.302). When we calculate the difference between the two, we get 275. Hence 275 is the correct answer and the others are incorrect.

7. A square is formed by sum of two _____________
a) Natural numbers
b) Consecutive Natural numbers
c) Alternate Natural numbers
d) Consecutive Whole numbers
View Answer

Answer: b
Explanation: When we add two consecutive natural numbers, we get a square (This happens in a few cases and not all cases). For example: 32=4+5=9.
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8. Which is the lower consecutive natural number forming the square 13?
a) 85
b) 84
c) 83
d) 82
View Answer

Answer: b
Explanation: The square of number 13 is formed by two consecutive natural numbers and they are 84 & 85. If we need to find the lower number (i.e.84 in this case) we can calculate like this, \(\frac{13^2-1}{2}=\frac{169-1}{2}=\frac{168}{2}\)=84.

9. (a-1)×(a+1)=_______
a) a2-1
b) a2+1
c) a2
d) a2+2
View Answer

Answer: a
Explanation: We have (a-1)×(a+1). Opening the brackets, we get,
(a-1)×(a+1)=(a2+a-a-1)=(a2-1). Hence, we conclude this (a-1)×(a+1) to be the correct answer.
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10. What would be the square of 11111?
a) 123454321
b) 1234321
c) 12321
d) 121
View Answer

Answer: a
Explanation: The numbers which have 1 in all the digits show a beautiful pattern.
For example: 112=121….1112=12321 and this goes on. This can be very helpful in finding squares.

Sanfoundry Global Education & Learning Series – Mathematics – Class 8.

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Manish Bhojasia - Founder & CTO at Sanfoundry
Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn | Youtube | Instagram | Facebook | Twitter