. CAT Question Paper Quants Slot 2 - CAT Sequence and Series Questions, 2IIM CAT 2022 Online Preparation for CAT, CAT coaching in Chennai | 2IIM CAT Online Coaching

CAT 2018 Question Paper | Quants Slot 2

CAT Previous Year Paper | CAT Sequence and Series Questions | Question 16

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

  1. 80707
  2. 80751
  3. 80730
  4. 80773

🎊 Independance Day Discount!
Upto 4,000 off on CAT Online Courses
Valid until 16th Aug


2IIM : Best Online CAT Coaching.


Video Explanation


Best CAT Coaching in Chennai


CAT Coaching in Chennai - CAT 2022
Limited Seats Available - Register Now!


Explanatory Answer

Method of solving this CAT Question from Sequence and Series

Here we have to find the value of the sum 7 × 11 + 11 × 15 + 15 × 19 + ..... + 95 × 99
Tn = (4n + 3) (4n + 7)
Since increment of 4 takes place in every value , 4n is the term to be used
T1 = (4 + 3) (4 + 7) = 7 × 11
T2 = 11 × 15
T3 = 15 × 19 and so on
Expanding Tn = (4n + 3) (4n + 7)
We will get 16n2 + 12n + 28n +21
16n2 + 40n +21
Σ16n2 + 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"

Hence, the answer is 80707

Choice A is the correct answer.

 

CAT Questions | CAT Quantitative Aptitude

CAT Questions | CAT DILR

CAT Questions | Verbal Ability for CAT


Where is 2IIM located?

2IIM Online CAT Coaching
A Fermat Education Initiative,
58/16, Indira Gandhi Street,
Kaveri Rangan Nagar, Saligramam, Chennai 600 093

How to reach 2IIM?

Phone: (91) 44 4505 8484
Mobile: (91) 99626 48484 / 94459 38484
WhatsApp: WhatsApp Now
Email: info@2iim.com