CAT Quantitative Aptitude Questions | CAT Algebra - Progressions questions

The question is about investments of a person which is in an AP. Another application based question from arithmetic progressions. With some simple but very powerful ideas, one can cut down on a lot of working when it comes to progressions. For example, anchoring a progression around its middle term can be very useful. CAT Exam tests the idea of progression often in the CAT Quantitative Aptitude section and this could also be tested in DI LR section of the CAT Exam as a part of a puzzle.

Question 16: Ram invests a total sum of 2000 rupees on government bonds in 4 years. If these investments are in A.P and the sum of squares of the investments is 1200000. Find the investment made by ram in each year respectively. It is also known that he always invest more than the previous year.

1. 200,400,600,800
2. 875,625,375,125
3. 125,375,625,875
4. 50,350,650,950

Explanatory Answer

Method of solving this CAT Question from CAT Algebra - Progressions: Make clear assumptions!

For solving these type of questions we must always take the numbers as
(a-3d),(a-d),(a+d),(a+3d)
So, Let the investment made by Ram in these years be (a-3d),(a-d),(a+d),(a+3d)
Then,
(a-3d) + (a-d) + (a+d) +(a+3d) = 2000
=> 4a = 2000
=> a = 500

Now, again \\frac{A}{Q}\\)
(a-3d)² +(a-d)² +(a+d)² +(a+3d)² = 1200000
=> 4(a² + 5 d²) = 1200000
=> (a² + 5 d²) = 300000
=> 250000 + 5d² = 300000
=> 5d² = 50000
=> d² = 10000
=> d = ±100

∴ d = 100 ( As the investment increases every year so d = -100 not possible)
Hence the investments made are 200,400,600,800

Note - If there are 3 number in series then take the numbers as (a-d),a,(a+d)
If there are 5 number in series then take the numbers as (a-2d),(a-d), a,(a+d),(a+2d)
…….. so on

While If there are 4 number in the series then take the numbers as (a-3d),(a-d), ,(a+d),(a+3d)
If there are 6 number in the series then take the numbers as (a-5d),(a-3d),(a-d), ,(a+d),(a+3d), (a+5d)
……………. so on

The question is "Find the investment made by ram in each year respectively. It is also known that he always invest more than the previous year."

Hence the answer is "200,400,600,800"

Choice A is the correct answer.