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No. 1

This week’s problem

1 and 36 are both square and triangular numbers. What is the next number that is both?

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The next is 12251225: it is 35235^2, and also the sum of the first 49 positive integers. A triangular number has the form n(n+1)/2n(n+1)/2. For n=49n=49, 49×50/2=122549\times50/2=1225. Checking the triangular numbers after 36 up to this point gives no earlier square.
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34\displaystyle \frac{3}{4}Three of four equal parts.
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Ramavana Mathematical Center
CBSE · Class 10

Real Numbers

Paper 0140 marks · 90 minutes

Section A · Multiple choice

2. The HCF of 40, 110 and 360 is

A. 40B. 110C. 360D. 10

Section B · Show your working

17. Using prime factorisation, find the HCF of 378 and 504.

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