# CAT 2021 Question Paper | Quant Slot 2

###### CAT Previous Year Paper | CAT Quant Questions | Question 16

CAT 2021 Quant was dominated by Arithmetic followed by Algebra. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 16 : For all real numbers x the condition |3x - 20| + |3x - 40| = 20 necessarily holds if

1. 6 < x < 11
2. 7 < x < 12
3. 10 < x < 15
4. 9 < x < 14

## Best CAT Coaching in Chennai

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

Let’s assume y to be 3x,
Now, the equation becomes | y - 20 | + | y - 40 | = 20
Let’s comprehend the meaning of | y - 20 |,
| y - 20 | simply means, the distance between y and 20
Let’s jot the three terms, y, 20 and 40 on a number line.

Now, y could be anywhere on the number line.
Observe that if y is on the left of 20, the distance between y and ‘40’ will be greater than 20 and the condition | y - 20 | + | y - 40 | = 20 fails.
If y is on the right of 40, the distance between y and ‘20’ will be greater than 20 and the condition | y - 20 | + | y - 40 | = 20 fails.
Hence the point y needs to be between 20 and 40.
Will any point between 20 and 40 qualify to be ‘y’ ?
Yes, Since the distance between 20 and 40 is exactly 20, for any ‘y’ between 20 and 40, the distance between 20 and ‘y’ plus the distance between ‘y’ and 40 is exactly 20.
So, 20 < y < 40
20 < 3x < 40
20/3 < x < 40/3
Option B alone holds good.
Alternate Solution:
We know that the minimum value of the modulus function can be zero.
Thus value occurs in the two modulus functions at 20/3 and 40/3 respectively.
So, for numbers less than 20/3 the value of both the functions increases and similarly, the value of the sum of the functions increases when x is greater than 40/3.
Between 20/3 and 40/3, the value of the functions remains the same as one of the inequality increases by the same amount as the decrease in the other.
So, the value of the sum of the modulus remains at 20 for the range of values [20/3 , 40/3].
Which can be rewritten as [6.66,13.33]
The option which satisfies this condition is 7 < x < 12.

The question is " For all real numbers x the condition |3x - 20| + |3x - 40| = 20 necessarily holds if "

##### Hence, the answer is '7 < x < 12'

Choice B is the correct answer.

###### CAT Coaching in ChennaiCAT 2024

Classroom Batches Starting Now! @Gopalapuram and @Anna nagar

###### Best CAT Coaching in Chennai

Attend a Demo Class

##### 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?

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