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Set X consists of prime numbers {3, 11, 7, K, 17, 19}. If integer Y

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Bunuel
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Set X consists of prime numbers {3, 11, 7, K, 17, 19}. If integer Y [#permalink] New post   14 Oct 2014, 05:54
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Tough and Tricky questions: Statistics.



Set X consists of prime numbers {3, 11, 7, K, 17, 19}. If integer Y represents the product of all elements in set X and if 11Y is an even number, what is the range of set X?

(A) 14
(B) 16
(C) 17
(D) 20
(E) 26
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C
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manpreetsingh86
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Re: Set X consists of prime numbers {3, 11, 7, K, 17, 19}. If integer Y [#permalink] New post   14 Oct 2014, 08:03
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Bunuel wrote:

Tough and Tricky questions: Statistics.



Set X consists of prime numbers {3, 11, 7, K, 17, 19}. If integer Y represents the product of all elements in set X and if 11Y is an even number, what is the range of set X?

(A) 14
(B) 16
(C) 17
(D) 20
(E) 26


y = product of all elements in set X. now, y will be even if 2 is part of this set (k=2), else y will be odd.

since we have, 11y as an even integer. therefore y must be even. (because 11 is odd, therefore the only way in which 11y can be even is when y is even.)

thus elements in the set X are {2,3,11,7,17,19} and thus its range is 19-2=17
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Set X consists of prime numbers {3, 11, 7, K, 17, 19}. If integer Y [#permalink] New post   14 Oct 2014, 10:03
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Bunuel wrote:

Tough and Tricky questions: Statistics.



Set X consists of prime numbers {3, 11, 7, K, 17, 19}. If integer Y represents the product of all elements in set X and if 11Y is an even number, what is the range of set X?

(A) 14
(B) 16
(C) 17
(D) 20
(E) 26


Since 11Y = Even therefore Y has to be EVEN since 11 is a odd integer (Even * Odd = Even)

Similarly, Y is the product of all integers in set X But all integers in Set X are odd except the unknown K and since X contains only prime numbers, K has to equal to 2... ( 2 is the only even prime number and the product of all prime numbers in set X has to be Even, Even * Odd = Even)

Since you know value of K you can calculate the range = Largest integer in the set minus Smallest integer in the set = 19-2 = 17

Answer is C
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Re: Set X consists of prime numbers {3, 11, 7, K, 17, 19}. If integer Y [#permalink] New post   14 Oct 2014, 19:47
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Bunuel wrote:

Tough and Tricky questions: Statistics.



Set X consists of prime numbers {3, 11, 7, K, 17, 19}. If integer Y represents the product of all elements in set X and if 11Y is an even number, what is the range of set X?

(A) 14
(B) 16
(C) 17
(D) 20
(E) 26


Just observe the numbers given in the set

{3, 11, 7, K, 17, 19}

All numbers are odd & prime, so there product is also odd

Given that 11y is even number (Again 11 is odd; so y has to be even)

The only prime number which is even = 2

So, for k = 2, range = 19-2 = 17

Answer = C
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Re: Set X consists of prime numbers {3, 11, 7, K, 17, 19}. If integer Y [#permalink] New post   14 Oct 2014, 19:53
One more method:

Just observe the OA

(A) 14
(B) 16
(C) 17
(D) 20
(E) 26

Once we are convinced that k = 2, then

Odd - Even = Odd

Only option C fits in; all other options are Even suggesting that "k" would be ODD which is not the case

Answer = C
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Re: Set X consists of prime numbers {3, 11, 7, K, 17, 19}. If integer Y [#permalink] New post   29 Jun 2018, 00:39
Bunuel wrote:

Tough and Tricky questions: Statistics.



Set X consists of prime numbers {3, 11, 7, K, 17, 19}. If integer Y represents the product of all elements in set X and if 11Y is an even number, what is the range of set X?

(A) 14
(B) 16
(C) 17
(D) 20
(E) 26


Bunuel,

How would we know whether 11Y is a 3 digit integer with unit digit as Y or it is a product of 11 * Y?
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Re: Set X consists of prime numbers {3, 11, 7, K, 17, 19}. If integer Y [#permalink] New post   29 Jun 2018, 01:24
Expert Reply
QZ wrote:
Bunuel wrote:

Tough and Tricky questions: Statistics.



Set X consists of prime numbers {3, 11, 7, K, 17, 19}. If integer Y represents the product of all elements in set X and if 11Y is an even number, what is the range of set X?

(A) 14
(B) 16
(C) 17
(D) 20
(E) 26


Bunuel,

How would we know whether 11Y is a 3 digit integer with unit digit as Y or it is a product of 11 * Y?


If it were a three-digit number it would have been explicitly mentioned. 11y is 11*y, recall that only * sign could be omitted.
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Re: Set X consists of prime numbers {3, 11, 7, K, 17, 19}. If integer Y [#permalink] New post   29 Jun 2018, 22:25
The product of 11Y is an even number, therefore Y would be even and if you look at the prime numbers in set X all are odd, therefore K would be even to get 11Y even. So we need an even number in the set, which would be K, lowest number.
As per equation: Range = Highest –Lowest
(A) 14 (19-14=5)
(B) 16 (19-16=3)
(C) 17 (19-17=2)
(D) 20 (not possible, greater than 19)
(E) 26 (not possible, greater than 19))
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Re: Set X consists of prime numbers {3, 11, 7, K, 17, 19}. If integer Y [#permalink] New post   25 Nov 2018, 00:47
Why should we consider k=2 only , why can’t we take k=4,6,8...
Plz help.

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Re: Set X consists of prime numbers {3, 11, 7, K, 17, 19}. If integer Y [#permalink] New post   21 Dec 2018, 22:07
11Y will be even if Y is even.
Y = product of all elements in the set.
There is no even no in the set X. So, ‘k’ should be even to make y even.
There is only one even prime no i.e. 2. So, k = 2
The set X becomes {2, 3, 7, 11, 17, 19}.
Range of the set = highest element – lowest element = 19 – 2 = 17
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Re: Set X consists of prime numbers {3, 11, 7, K, 17, 19}. If integer Y [#permalink] New post   31 Dec 2018, 00:53
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DivyaYerranagula wrote:
Why should we consider k=2 only , why can’t we take k=4,6,8...
Plz help.

Posted from my mobile device


Hi Divya

We cannot take any other even nos because they are not primes and it is clearly mentioned that set consists of prime nos and integer 2 is the only even prime no.

Hope it helps
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Re: Set X consists of prime numbers {3, 11, 7, K, 17, 19}. If integer Y [#permalink] New post   02 Mar 2019, 09:20
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Bunuel wrote:

Tough and Tricky questions: Statistics.



Set X consists of prime numbers {3, 11, 7, K, 17, 19}. If integer Y represents the product of all elements in set X and if 11Y is an even number, what is the range of set X?

(A) 14
(B) 16
(C) 17
(D) 20
(E) 26



Since 11Y is even, Y is even and hence K must be even also. Since 2 is the only even prime number, K is 2. Thus, the range of set X is 19 - 2 = 17.

Answer: C
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Re: Set X consists of prime numbers {3, 11, 7, K, 17, 19}. If integer Y [#permalink] New post   02 Nov 2021, 10:30
What does it mean that integer y represents the product of all elements in set X?

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Re: Set X consists of prime numbers {3, 11, 7, K, 17, 19}. If integer Y [#permalink]
02 Nov 2021, 10:30
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