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Tricky Exponents!!
The ‘Prime’ Importance of Prime Numbers
March 13, 2016
Integrated Reasoning
May 23, 2016
In some previous articles we have learnt about a few interesting concepts on exponents. In this piece of articulation let us enjoy some exam focused properties of the tricky exponent!
23 = 2 x 2 x 2
But this could also be written as 23 = 22 x 2; also, multiplication is addition that many number of times. Eg: 2 x 3 = 2 + 2 + 2.
Likewise, for the first equation, we can write, 23 = 22 + 22.
In order to generalise it, 35 = 34 x 3, or 34 + 34 + 34 or
57= 56 x 5 = 56 + 56 +56 +56 +56
This property is extensively used in standardised tests:
- If, 2m + 2n = 240 find the value of (m + n) , where, m & n are integers.
- 40
- 60
- 78
- 80
- 158
Solution:
Using the same property, we have 2m + 2n = 240 = 239 x 239.
This is the only combination whose sum will give 240.
Thus, m & n = 39
m + n = 39 + 39 = 78
Answer: C
- If, 3x x 3y x 3z = 312, where x, y & z are integers. Find the highest prime factor of xyz.
- 3
- 5
- 11
- 13
- 127
Solution:
Same logic, so, 312 = 311 + 311 + 311 ;
Thus, possible values for x,y & z = 11, 11 and 11.
xyz = 11 x 11 x 11 = 113
The highest prime factor of is 113 is 11.
Answer: C
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