Join 60,000+ competitive exam aspirants
or with email
Your Cart
SubtotalтВ╣0
TotalтВ╣0
Examoogle тАв User тАв info@examoogle.com тАв EE-2024-8821
Chapter 1 of 12 тАв Page 1 of 248ЁЯФТ Protected PDF тАв Watermarked
Join 60,000+ competitive exam aspirants
The value of 123тИТ73 is:
1385
1728
1085
1485
1385
Check the unit digit: 123 ends in 8 and 73 ends in 3. Therefore, 8тИТ3=5. Only option A ends with 5.
We are given two cubes of integers, 12 and 7, and we need to find the difference between their cubes, 12┬│ - 7┬│.
a3тИТb3=(aтИТb)(a2+ab+b2)
Check the unit digit: 123 ends in 8 and 73 ends in 3. Therefore, 8тИТ3=5. Only option A ends with 5.
Calculating the cubes individually (1728тИТ343) is time-consuming and prone to arithmetic errors compared to using the algebraic identity.
Identify terms
Identify a=12 and b=7 for the algebraic identity a3тИТb3.
a=12,b=7
Apply algebraic identity
Substitute the values into the formula (aтИТb)(a2+ab+b2).
(12тИТ7)(122+12├Ч7+72)
Calculate components
Calculate the difference (12тИТ7)=5 and the sum of the square terms 144+84+49=277.
5├Ч277
Final product
Multiply the results: 5├Ч277=1385.
5├Ч277=1385
A is correct because the difference 1728тИТ343 equals 1385.
Using (aтИТb)(a2+ab+b2) is significantly faster than long multiplication, a technique essential for clearing competitive aptitude sections under time pressure.
Get instant step-by-step AI explanations, full shift Previous Year Papers (SSC GD, RRB, SSC JE), and regional rank analysis on the official Examoogle App.
Free Download тАв 100K+ Aspirants