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A set of numbers has the property that for any number t in the set, t + 2 is in the set. If -1 is in the set, which of the following must also be in the set?

I. -3 II. 1 III. 5

(A) I only (B) II only (C) I and II only (D) II and III only (E) I, II , and III

Problem Solving Question: 158 Category:Arithmetic Properties of numbers Page: 83 Difficulty: 600

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A set of numbers has the property that for any number t in the set, t + 2 is in the set. If -1 is in the set, which of the following must also be in the set?

I. -3 II. 1 III. 5

(A) I only (B) II only (C) I and II only (D) II and III only (E) I, II , and III

The question is which of the following must be in the set, not could be in the set.

If -1 is in the set so must be -1+2=1, as 1 is in the set so must be 1+2=3, as 3 is in the set so must be 3+2=5 and so on. So basically knowing that -1 is in the set we can say that ALL odd numbers more than -1 are also in the set.

Re: A set of numbers has the property that for any number t in t [#permalink]

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04 Jun 2014, 22:39

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Tricky one ! The idea here is the *MUST* condition makes it strict to move forward from the seed number -1 since for any t , t+2 exists. The set could start from -1 and not have -3 in it.

Re: A set of numbers has the property that for any number t in t [#permalink]

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12 Apr 2015, 07:15

But how could we assume that the set has n numbers in it when it is not given.. The set could also have -1 and 1 alone with 2 numbers in that set. Also if we assume that it could have 3 as well, then why could not we assume that -3 is also in that set, as they dint pinpoint that -1 is the starting number in that set. The starting number can also be -3.. I know its a must be not could be question.. But unless we know the starting number and number of elements perfectly, it will become could be question..

A set of numbers has the property that for any number t in t [#permalink]

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12 Apr 2015, 08:33

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sheolokesh wrote:

But how could we assume that the set has n numbers in it when it is not given.. The set could also have -1 and 1 alone with 2 numbers in that set. Also if we assume that it could have 3 as well, then why could not we assume that -3 is also in that set, as they dint pinpoint that -1 is the starting number in that set. The starting number can also be -3.. I know its a must be not could be question.. But unless we know the starting number and number of elements perfectly, it will become could be question..

Maybe I can explain this. Don't know how much of this will be helpful.

The point here is -1 is our reference number i.e. t= -1 Now, since the question is "MUST BE TRUE", we have to find numbers that "RESULT FROM" the operation t+2.

When you say that -3 is present (it could be), we are in fact saying that the operation t+2 "RESULTS IN" the number -1. So here we are making t+2 the reference value and -1 the result of the operation.

In a vague way, when we say Ron is Sam's brother, its not necessary that Sam is also Ron's brother. Sam could be Ron's sister too.

Re: A set of numbers has the property that for any number t in t [#permalink]

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13 Apr 2015, 03:54

Ashishmathew01081987 wrote:

sheolokesh wrote:

But how could we assume that the set has n numbers in it when it is not given.. The set could also have -1 and 1 alone with 2 numbers in that set. Also if we assume that it could have 3 as well, then why could not we assume that -3 is also in that set, as they dint pinpoint that -1 is the starting number in that set. The starting number can also be -3.. I know its a must be not could be question.. But unless we know the starting number and number of elements perfectly, it will become could be question..

Maybe I can explain this. Don't know how much of this will be helpful.

The point here is -1 is our reference number i.e. t= -1 Now, since the question is "MUST BE TRUE", we have to find numbers that "RESULT FROM" the operation t+2.

When you say that -3 is present (it could be), we are in fact saying that the operation t+2 "RESULTS IN" the number -1. So here we are making t+2 the reference value and -1 the result of the operation.

In a vague way, when we say Ron is Sam's brother, its not necessary that Sam is also Ron's brother. Sam could be Ron's sister too.

Hope so it clears some of your doubt.

Yes that's fine.. But there is another clarification need to be done in my question... How could we say 5 must be in the set unless we know the number of elements in the set then.. I have entwined presence of 5 and -3 here.. If 5 is a must be present, then we are assuming the set has 3+ elements.. But what if the set has only 2 elements of 1 and 3 alone..? isnt that an presumption then?

A set of numbers has the property that for any number t in the set, t + 2 is in the set. If -1 is in the set, which of the following must also be in the set?

I. -3 II. 1 III. 5

(A) I only (B) II only (C) I and II only (D) II and III only (E) I, II , and III

The question is which of the following must be in the set, not could be in the set.

If -1 is in the set so must be -1+2=1, as 1 is in the set so must be 1+2=3, as 3 is in the set so must be 3+2=5 and so on. So basically knowing that -1 is in the set we can say that ALL odd numbers more than -1 are also in the set.

Answer: D.

Hi Bunuel, Can you please explain the mathematical distinction between MUST be and COULD be question stems? I don't understand that.

Must be true means that something should be true for ANY (ALL) value (cases). Could be true means that something could be true for SOME (at least one) value (case).

Would the answer be E, Had the question have "could be" instead of "must be"?

I am confused why E is not the answer.

If -1 is the source integer in the set, so if -1 is the smallest integer in the set, then -3 will not be in the set. For example, the set could be {-1, 1, 3, 5, 7, ...}. So, again, knowing that -1 is in the set we can say that ALL odd numbers more than -1 are also in the set but we cannot be sure about the numbers less than -1.