GATE Civil 2024 Set 1 | GA | Question: 4

Question

​Which one of the given options is a possible value of $x$ in the following sequence?
\[
3,7,15, x, 63,127,255
\]

• A. $35$
• B. $40$
• C. $45$
• D. $31$

Comments

How to think ?

 

Answer 1

Method - 1:

$3, \, 7, \, 15, \, x, \, 63, \, 127, \, 255$

$\Rightarrow 2^{2} - 1, \, 2^{3} - 1, \, 2^{4} - 1, \, x, \, 2^{6} - 1, \, 2^{7} - 1, \, 2^{8} - 1$

hence,  $x = 2^{5} - 1 = 32 - 1 = 31$

Method - 2:

$3, \, 7, \, 15, \, x, \, 63, \, 127, \, 255$

$\Rightarrow 3, \, 3 \times 2 + 1, \, 7 \times 2 + 1, \, 15 \times 2 + 1, \, 31 \times 2 + 1, \, 63 \times 2 + 1, \, 127 \times 2 + 1$

hence,  $x = 15 \times 2 + 1 = 30 + 1 = 31$

Method - 3:

$3, \, 7, \, 15, \, x, \, 63, \, 127, \, 255$

$7-3, \, 15-7, \, x- 15, \, 63-x, \, 127-63, \, 255-127$

$\Rightarrow 7-3, \, 15-7, \, x- 15, \, 63-x, \, 127-63, \, 255-127$

$\Rightarrow 4, \, 8, \, x-15, \, 63-x, \, 64, \, 128$

$\Rightarrow 4 \times 1, \, 4\times 2^{1}, \, x-15, \, 63-x, \, 4 \times 2^{4}, \, 4 \times 2^{5}$

similar G.P. :  $4 \times 1, \, 4\times 2^{1}, \, 4 \times 2^{2}, \, 4 \times 2^{3}, \, 4 \times 2^{4}, \, 4 \times 2^{5}$  $(a=4, \, r=2)$

hence,  $x - 15 = 4 \times 2^{2}$

$\Rightarrow x - 15 = 4 \times 4$

$\Rightarrow x - 15 = 16$

$\Rightarrow x = 31$

Comments

@ankitgupta.1729
I was not referring to the actual rules of the GATE exam, but rather to the ways in which the questions are designed. It seems that they make certain assumptions about the aspirants' interpretation of the questions, based on the knowledge they are expected to have at an undergraduate level. While I agree that assumptions about the aspirants' knowledge and understanding should be avoided, as not all are fresh undergraduates and some may have enhanced their knowledge in the industry, the questions should be designed without presumptions, based solely on rigorous concepts, whether mathematical or otherwise. However, until we reach that ideal, we must interact with the system as it exists, abide by its rules, and simultaneously advocate for the creation of questions based purely on rigorous concepts.

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@ankitgupta.1729

Previously, my comments were aimed at aspirants like me who may not have as extensive knowledge as you do. However, since you appear to have a thorough understanding of the subject, could you guide us in addressing our concerns to the GATE committee? This way, we can ensure such questions are not included in future examinations.

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(1/2)

@anujs

This is not about the knowledge or any mathematical rigorous concepts.

If you put x="Modi Ji" then it is still a sequence. Particularly it is called a sequence of objects in which some are integer objects and some are strings.

Now, here you have not used any mathematical rigorous concept or any extensive knowledge, Neither I have used it in above comment to show each option is correct.

Even if you see Math.Stackexchange where some university professors are also there, says that these type of question should not be asked.

These type of questions are coming from many years, not in gate but in other exams also. 

Not only these type of question, if you look carefully, there are many mistakes in question paper from last couple of years in gate that I have observed some questions because I am not in touch with gate subjects.

You can just see this year paper of gate 2024 for all branches (including DA paper where 4 questions are straight wrong till now) and see the mistakes.

In mechanical paper, they have given 3 MTAs in the first answer key which tells about the quality of paper by IITs and IISc professors.

Even this is fine, if some student lose his/her time in exam that is also fine but at least accept the mistakes, after the challenge, they neither accept their mistakes nor give the reason for rejecting the challenge. It is sad to see even if one student lose the marks even if he/she is logically correct.

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(2/2)

Now your question is how to solve this issue ?

Few months back one IIT-K alumnus Dheeraj Singh got the unemployment information of IITs through an RTI and taggeed the directors of many IITs but nothing happened.
Young people are suiciding every year, this same guy also tried to take some initiative and tagged many IITs in his post to overcome this issue but nothing happened.
Few months back an old retired gardener got suicide because his gratuity got denied by IIT-B administration.

These are few issues that I know from last few months and these are somewhat bigger than the issue of wrong questions of exams though comparison should not have to be done.
But you can see the system in india for bigger issues like unemployment, suicides etc.

In my opinion, some improvement can be done if some mass protest can be done regarding this issue and issue goes to Supreme Court and it might be possible when many coaching institutes come forward if they are not busy with their marketing business to attract students. But the problem is
very few students might get affected and most of the time system doesn't care if some students got affected even those marks are important for them.

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@ankitgupta.1729

I hear you, brother. you're right - these problems are much bigger than just exam questions. it's really sad to see so many serious issues being ignored by these big institutions, especially when they're hurting lakhs of students and even their own staff.

I can feel how frustrated you are feeling because of this whole system. it sure is not easy to see these problems keep happening again and again without any real change.

I really appreciate you for speaking up so openly about all this and even if it feels like nothing's changing, I want to assure you that your words matter. you're helping us all see the bigger picture of a much bigger and deeper issue. let's keep talking about all these issues like this again and again - maybe if enough of us speak up like this, someday things will get better.