Question 4 the day : June 4, 2002

When you take CAT, what makes a crucial difference in determining whether you crack CAT and get into the IIM s or not is how quick you can attempt questions.

One of the key observations that might throw light on CAT cracking methodologies is that - in most cases students spend about 60% of the time in quant and DI section on calculations. If you can make a difference to your calculation speed, even if it is marginal, it will make a substantial difference to your getting into an IIM. After all people make it to the cut off by a margin of 0.25 marks.

We will intersperse our question a day with a fast calculation tip every now and then and about 5 exercise problems for each method. Practice speed calculation whenever you have to calculate anything. Engineers particularly, should try and throw their fx 100 calculators away, at least, for the time being. And commerce graduates do not go anywhere near your calculators for the next 6 months.

Tip 1

If you have to find the square of numbers ending with '5'.

e.g 25 * 25. Find the square of the units digit (which is 5) = 25. Write this down.
Then take the tenths digit (2 in this case) and increment it by 1 (therefore, 2 becomes 3). Now multiply 2 with 3 = 6.
Write '6' before 25 and you get the answer = 625.

For instance, if you have to find the square of 45. 45 * 45.
The square of the units digit =- 25
Increment 4 by 1. It will give you '5'. Now multiply 4 * 5 = 20. Write 20 before 25. The answer is 2025.

In the case of numbers like 125. The rule applies without an iota of difference.
The square of the units digit = 25.
Increment 12 by 1. It will give you 13. Now multiply 12*13 = 156. Write 156 before 25. The answer is 15625.

Try out the above technique with the following numbers.

Questions

1. 225 * 225
2. 75 * 75
3. 145 * 145
4. 35 * 35
5. 375 * 375.

Answers and Explanations

1. 225 * 225. Square of units digits is 25. Increment 22 by 1 to get 23. The product of 22 and 23 is 506. Therefore, the answer is 50625.
2. 75 * 75. Square of the units digits is 25. Increment 7 by 1 to get 8. The product of 7*8 = 56. Therefore, the answer is 5625.
3. 145 * 145. Square of the units digits is 25. Increment 14 by 1 to get 15. The product of 14*15 = 210. Therefore, the answer is 21025.
4. 35 * 35. Square of the units digits is 25. Increment 3 by 1 to get 4. The product of 3*4=12. Therefore, the answer is 1225.
5. 375 * 375. Square of the units digits is 25. Increment 37 by 1 to get 38. The product of 37*38=1406. Therefore, the answer is 140625.

1. Factors, divisors; Prime Factors		2. Test of divisibility by 3, 4, 5 and 7
3. Framing equation : Word Problem		4. Operations on odd and even numbers
5. Remainders of division by a factor of 'd'		6. Sum of first 'n' natural numbers : AP
7. Number of factors of a positive integer		8. Is 1025 - 7 divisible by 3?
9. How to find the HCF / GCD of numbers?		10. Test of Divisibility by 8 and 11.
11. Number Properties : Products		12. Numbers, Fractions - TANCET '08
13. LCM, Number theory - XAT 2012		14. Number of divisors / factors
15. Highest power dividing a factorial		16. Right Triangles - Squares of numbers
17. Comparing Numbers : TANCET 2008

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