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# M23-28

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 01:19
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81% (00:22) correct 19% (00:20) wrong based on 107 sessions

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Are all elements of set $$S$$ smaller than 40 ?

(1) The smallest element of $$S$$ is -1

(2) The range of $$S$$ is 41

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 01:19
Official Solution:

(1) The smallest element of $$S$$ is -1. Clearly insufficient.

(2) The range of $$S$$ is 41. Clearly insufficient.

(1)+(2) The range is the difference between the largest and the smallest elements of a set, so we have that $$41=\{ \text{largest element}\}-(-1)$$, which gives that $$\{ \text{larges element}\}=40$$, so not all element of set $$S$$ are smaller than 40. Sufficient.

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23 Mar 2018, 12:35
well i believe its E, since over here if we combine both the statements & the range is 41 ( which means 1st element of the set minus last element of the set), if 1st element is -1, last could be 42 in which case the range is 41 & its true but if the last element in S set is 40, then the result is 39 so even after combining the statements, we cant conclude it so its E since we don't know the last element of the set.
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23 Mar 2018, 12:45
imtisalsiddiqui wrote:
well i believe its E, since over here if we combine both the statements & the range is 41 ( which means 1st element of the set minus last element of the set), if 1st element is -1, last could be 42 in which case the range is 41 & its true but if the last element in S set is 40, then the result is 39 so even after combining the statements, we cant conclude it so its E since we don't know the last element of the set.

It's a math question and the answer is C. It's not a matter of belief.

1. A set by definition has no order.

2. (1) says that the smallest element of S is -1 and (2) says that the range of S is 41. The range = Largest element - Smallest element: 41 = Largest element - (-1). Thus, Largest element = 40. So, the answer to the question whether all the elements of set S are smaller than 40 is NO.

3. If the Largest element were 42, then the range would have been 43, NOT 41.
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28 Mar 2018, 15:08
I think this the explanation isn't clear enough, please elaborate. Why is statement 2 not sufficient, if you pick 42 and 1 the range is 41 and S has a number that is greater than 40, similarly if we pick 40 and -1 the range is 41.
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28 Mar 2018, 20:46
AMARAAZUNWIE wrote:
I think this the explanation isn't clear enough, please elaborate. Why is statement 2 not sufficient, if you pick 42 and 1 the range is 41 and S has a number that is greater than 40, similarly if we pick 40 and -1 the range is 41.

For (2) all we know is that the range of the set is 41. How can this be sufficient to say whether all elements of the set are less than 40? If the set is {-141, -100} the answer is YES but if the set is say {100, 141} then the answer is NO.
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13 May 2018, 03:00
Hi Bunuel,

Can you please see, if my explanation is approach was correct.

Statement: -1 Clearly Insufficient.

Statement: The range of Set S is 41, this is insufficient because lets say:
If smallest integer is -4 and biggest integer is 37, then Range is 41 and answer is Yes.

But if smallest integer is -1 and biggest integer is 40, then Range is 41 and answer is No.

C, removes the first case thus sufficient.
Re: M23-28   [#permalink] 13 May 2018, 03:00
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# M23-28

Moderators: chetan2u, Bunuel

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