You can expect at least one question from **Sequences and Series** topic in the CAT Exam. This CAT 2018 Question Paper is no exception. Make sure you are doubly thorough with your concepts while taking up the CAT Online Preparation. CAT Quants require some specific strateges, and to learn about the preparation techniques, click: **How to prepare for Quant**.

Question 16 : The value of the sum 7 x 11 + 11 x 15 + 15 x 19 + ..... + 95 x 99 is

- 80707
- 80751
- 80730
- 80773

Limited Seats Available - Register Now!

Here we have to find the value of the sum 7 × 11 + 11 × 15 + 15 × 19 + ..... + 95 × 99

T_{n} = (4n + 3) (4n + 7)

Since increment of 4 takes place in every value , 4n is the term to be used

T_{1} = (4 + 3) (4 + 7) = 7 × 11

T_{2} = 11 × 15

T_{3} = 15 × 19 and so on

Expanding T_{n} = (4n + 3) (4n + 7)

We will get 16n^{2} + 12n + 28n +21

16n^{2} + 40n +21

Σ16n^{2} + 40 Σn + 21 Σ1

\\frac{16n(n+1)(2n+1)}{6}) + \\frac{40n(n+1)}{2}) + 21 × n

Simplifying this we can take n out

n[\\frac{8n(n+1)(2n+1)}{3}) + 20(n+1) + 21]

From the options we can take 80707 and check whether it is divisible by 23

\\frac{80707}{23}) = 3509

⟹ option a) 80707 is a multiple of 23

⟹ option b) 80751 is 80707 + 44 so this doesn’t work

⟹ option c) 80730 is 80707 + 23 so this is also a multiple of 23

⟹ option d) 80773 is 80707 + 66 so this also doesn’t work

So let us check out with option a and c so we have to substitute and simplify and find

n[\\frac{8n(n+1)(2n+1)}{3}) + 20(n+1) + 21]

\\frac{n}{3})[8(n+1)(2n+1) + 60(n+1) + 63]

From the answer choices we have only two possibilities left out i.e. 23 ⨯ 3509 or 23 ⨯ 3510

⟹ \\frac{23}{3})[8(23 + 1)(2(23) + 1) + 60(23 + 1) + 63]

⟹ \\frac{23}{3})[8(24)(47) + 60 (24) + 63]

⟹ \\frac{23}{3})[8(24)(47) + 60 (24) + 63]

⟹ 23[8(8)(47) + 60 (8) + 21]

⟹ 80707

Hence the value of the sum 7 × 11 + 11 × 15 + 15 × 19 + ..... + 95 × 99 is 80707

The question is **"The value of the sum 7 x 11 + 11 x 15 + 15 x 19 + ..... + 95 x 99 is"**

Choice A is the correct answer.

Copyrights © All Rights Reserved by 2IIM.com - A Fermat Education Initiative.

Privacy Policy | Terms & Conditions

CAT^{®} (Common Admission Test) is a registered trademark of the Indian Institutes of Management. This website is not endorsed or approved by IIMs.

2IIM Online CAT Coaching

A Fermat Education Initiative,

58/16, Indira Gandhi Street,

Kaveri Rangan Nagar, Saligramam, Chennai 600 093

**Mobile:** (91) 99626 48484 / 94459 38484

**WhatsApp:** WhatsApp Now

**Email: **info@2iim.com