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For a certain set of numbers, if x is in the set, then x 3 is also

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jayoptimist
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For a certain set of numbers, if x is in the set, then x 3 is also [#permalink] New post   Updated on: 08 Nov 2023, 07:18
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For a certain set of numbers, if x is in the set, then x – 3 is also in the set. If the number 1 is in the set, which of the following must also be in the set?

I. 4
II. -1
III. -5

A. I only
B. II only
C. III only
D. I and II
E. II and III

PS00253

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I need to know why can't x-3 = 1 be considered? if yes then x = 4 (which is not the answer :? )
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C

Originally posted by jayoptimist on 30 Jul 2012, 07:45.
Last edited by Bunuel on 08 Nov 2023, 07:18, edited 4 times in total.
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Re: For a certain set of numbers, if x is in the set, then x 3 is also [#permalink] New post   30 Jul 2012, 08:02
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jayoptimist wrote:
For a certain set of numbers, if x is in the set, then x - 3 is also in the set. If the number 1 is in the set , which of the following must also be in the set ?

a) 4
b) -1
c) -5

A. a only,
B. b only,
C. c only,
D. a and b only
E. b and c only

I need to know why can't x-3 = 1 be considered? if yes then x = 4 (which is not the answer :? )


Notice that the question asks which of the following MUST be in the set, not COULD be in the set.

Since 1 is in the set, then so must be 1-3=-2. Similarly, since -2 is in the set, then so must be -2-3=-5. Could 4 and -1 be in the set? Certainly, but we don't know that for sure.

Answer: C.

Regarding your question: we don't know which is the source integer in the set, if it's 1, then 4 won't be in the set but if the source integer is say 7, then 4 will be in the set. So, 4 may or may not be in the set.

Similar questions to practice:
a-set-of-numbers-has-the-property-that-for-any-number-t-in-t-98829.html
k-is-a-set-of-integers-such-that-if-the-integer-r-is-in-k-103005.html

P.S. Please read and follow: rules-for-posting-please-read-this-before-posting-133935.html (rule #3).
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Re: For a certain set of numbers, if x is in the set, then x 3 is also [#permalink] New post   26 Jul 2017, 16:32
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jayoptimist wrote:
For a certain set of numbers, if x is in the set, then x - 3 is also in the set. If the number 1 is in the set , which of the following must also be in the set ?

a) 4
b) -1
c) -5

A. a only,
B. b only,
C. c only,
D. a and b only
E. b and c only


'If we let x = 1, then (1 - 3) = -2 is in the set. If -2 is in the set, then (-2 - 3) = -5 is in the set. We can see that if we keep subtracting 3, we will get terms such as -8, -11, -14, etc. We see that -5 is definitely in the set, but -1 isn’t, since if 1 and -2 are in the set, then any numbers between them can’t be in the set.

Note: some people might argue that 4 is also in the set, since if we let x - 3 = 1, then x = 4. Of course, the answer choices don’t have ‘a and c only’ as an option. The problem says: “if x is in the set, then x - 3 is also in the set.” The problem doesn’t say: “if x - 3 is in the set, then x is also in the set.” So, when the problem says “if the number 1 is in the set,” we have to assume that 1 is the value of x, and we have to subtract 3 and keep subtracting 3 to get subsequent terms. We can’t assume that 1 is the value of x - 3.

Answer: C
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Re: For a certain set of numbers, if x is in the set, then x 3 is also [#permalink] New post   30 Dec 2012, 17:22
For a certain set of numbers, if x is in the set, x-3 is also in the set. If the number 1 is in the set, which of the following must also be in the set
I) 4
II) -1
III) -5

the answer is III only, means -5.

They are reasoning that, 1 in the set, so -2 also in the set, so -5 also in the set, so -8 also in the set.

I wonder why 4 can't be in the set??? let consider 1 is x-3, not x, hence x = 4.
What is the trap of GMAT here?

(I always have problem with the trap of gmat)
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Re: For a certain set of numbers, if x is in the set, then x 3 is also [#permalink] New post   30 Dec 2012, 21:40
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akhandamandala wrote:
For a certain set of numbers, if x is in the set, x-3 is also in the set. If the number 1 is in the set, which of the following must also be in the set
I) 4
II) -1
III) -5

the answer is III only, means -5.

They are reasoning that, 1 in the set, so -2 also in the set, so -5 also in the set, so -8 also in the set.

I wonder why 4 can't be in the set??? let consider 1 is x-3, not x, hence x = 4.
What is the trap of GMAT here?

(I always have problem with the trap of gmat)


We can look at this as a cause and effect problem. "x" is the cause and "x-3" is the effect. i.e. We are given that is "x" is in the set "x-3" is also in the set. The reverse need not necessarily be true. We cannot take the effect to be the cause.
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Re: For a certain set of numbers, if x is in the set, then x 3 is also [#permalink] New post   31 Dec 2012, 12:21
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jayoptimist wrote:
For a certain set of numbers, if x is in the set, then x - 3 is also in the set. If the number 1 is in the set , which of the following must also be in the set ?

a) 4
b) -1
c) -5

A. a only,
B. b only,
C. c only,
D. a and b only
E. b and c only

I need to know why can't x-3 = 1 be considered? if yes then x = 4 (which is not the answer :? )


I call them Verbal diaorea of GMAT. You have to follow these verbal vomits carefully. When they say x-3 is there only x-3 is guaranteed to be there nothing else. And so here you can not travel to the side of the stream.
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Re: For a certain set of numbers, if x is in the set, then x 3 is also [#permalink] New post   31 Dec 2012, 17:56
maibhihun wrote:
jayoptimist wrote:
For a certain set of numbers, if x is in the set, then x - 3 is also in the set. If the number 1 is in the set , which of the following must also be in the set ?

a) 4
b) -1
c) -5

A. a only,
B. b only,
C. c only,
D. a and b only
E. b and c only

I need to know why can't x-3 = 1 be considered? if yes then x = 4 (which is not the answer :? )


I call them Verbal diaorea of GMAT. You have to follow these verbal vomits carefully. When they say x-3 is there only x-3 is guaranteed to be there nothing else. And so here you can not travel to the side of the stream.


that's true, I have no problem with math, but I have quite problem with those kinds of "Verbal diaorea of GMAT". Hope exercises will help much. Thanks
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Re: For a certain set of numbers, if x is in the set, then x 3 is also [#permalink] New post   27 Apr 2014, 09:18
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It does not make logical sense to only have -5 and 4 is not the correct answer.

Can't we take that 1 is the result of X -3 ? In which case, X = 4.

I cant agree with -5 more because it is one more "jump"

X = 1 .... 2nd number is ( -2 ) is fine with me.
But the question did not say that "X - 6" also exists? Because X is still 1, and did not "move on" to become -2.

Agree its a bit of a "throw you off if you did not buy our official guide" even if you had maths as your bach degree.

Hope this kind of stuff don't pop up for my coming exam, but it cant be helped =)
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Re: For a certain set of numbers, if x is in the set, then x 3 is also [#permalink] New post   20 Dec 2020, 07:04
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jayoptimist wrote:
For a certain set of numbers, if x is in the set, then x - 3 is also in the set. If the number 1 is in the set , which of the following must also be in the set ?

a) 4
b) -1
c) -5

A. a only,
B. b only,
C. c only,
D. a and b only
E. b and c only


1 is in the set, so: 1-3=-2; -2-3=-5 are in the set.

There is no chance that any positive number other than 1 will be in the set according to the given condition.
And the negative value is also increasing.

The answer is \(C\)
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Re: For a certain set of numbers, if x is in the set, then x 3 is also [#permalink] New post   20 Dec 2020, 08:03
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For x: x-3 is in the set

For 1: 1 - 3 = -2 is in the set

For -2: -2 - 3 = -5 is in the set

We aren't sure of other numbers.

Answer C
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Re: For a certain set of numbers, if x is in the set, then x 3 is also [#permalink] New post   29 Apr 2022, 07:54
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jayoptimist wrote:
For a certain set of numbers, if x is in the set, then x - 3 is also in the set. If the number 1 is in the set , which of the following must also be in the set ?

a) 4
b) -1
c) -5

A. a only,
B. b only,
C. c only,
D. a and b only
E. b and c only

Show Spoiler
I need to know why can't x-3 = 1 be considered? if yes then x = 4 (which is not the answer :? )


Important: This IF-THEN statement only goes in one direction. That is, IF x is in the set, THEN x-3 is also in the set.
So, since we're told 1 is in the set, it must also be true that 1-3 (aka -2) is also in the set.
Now that we know -2 is in the set, it must also be true that (-2)-3 (aka -5) is also in the set.
Now that we know -5 is in the set, it must also be true that (-5)-3 (aka -8) is also in the set.
And so on. . . .
So, -5 is the only number (among the answer choices) that we KNOW must be in the set

Answer: C

Note: Some students will (incorrectly) conclude that the given information ALSO tells us that IF x-3 is in the set, THEN x is also in the set.
These students will (incorrectly) conclude that, if 1 is in the set, then 4 must also be in the set.
Think of it this way: If an animal is a dog, then that animal has ears (I think we all agree with us). We can't then take this statement and ALSO conclude that if an animal has ears, then that animal must be a dog
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Re: For a certain set of numbers, if x is in the set, then x 3 is also [#permalink] New post   21 Jul 2023, 10:05
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