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13 Jul 2018, 00:53
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Difficulty:
95%
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Question Stats:
40% (02:51) correct
60%
(02:47)
wrong
based on 348
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Set X consists of the positive multiples of 5, and set Y consists of the odd prime numbers less than 20. If set Z consists of every distinct integer less than 100 that is the product of one element from set X and one element from set Y, then set Z consists of how many elements?
A. 12
B. 14
C. 15
D. 16
E. 18
A. 12
B. 14
C. 15
D. 16
E. 18
13 Jul 2018, 03:33
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x: {5;10;15;20;25;30;35...}
y: {3;5;7;11;13;17;19}
To find z, let's take the first value of x, 5. It can be multiplied by all 7 values of y as the result will be less than 100.
When x = 10, we can multiply it only by the first 3 values of y, otherwise it will be greater than 100.
When x = 15, only by the first 2.
When x = 20, only by the first one.
When x = 25, only by the first one.
When x = 30, only by the first one.
For x greater than 30, we cannot multiply it by any value of y or it will exceed 100.
There is a total of 7+3+2+1+1+1 = 15 possible values, but be careful with the duplicate value of 75 (15*5 and 25*3) as the set must consist of distinct integers. Therefore the value is 14.
Answer B.
y: {3;5;7;11;13;17;19}
To find z, let's take the first value of x, 5. It can be multiplied by all 7 values of y as the result will be less than 100.
When x = 10, we can multiply it only by the first 3 values of y, otherwise it will be greater than 100.
When x = 15, only by the first 2.
When x = 20, only by the first one.
When x = 25, only by the first one.
When x = 30, only by the first one.
For x greater than 30, we cannot multiply it by any value of y or it will exceed 100.
There is a total of 7+3+2+1+1+1 = 15 possible values, but be careful with the duplicate value of 75 (15*5 and 25*3) as the set must consist of distinct integers. Therefore the value is 14.
Answer B.
18 Jul 2019, 19:38
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First let us define the set -
Set A = {5n} where n = 1,2,3, .....
Set B = {3 , 5 , 7 , 11 , 13 , 17}
Now Set Z is just product of all element of A and B
(Note: Its product of a all possible combination in A and B. But we have defined only one element in A so problem has got much easy.
)
So,
Set Z = {15n , 25n , 35n , 55n , 65n , 85n)
To satisfy condition of Z < 100
15n < 100 .... can give us max 6 numbers
25n < 100 .... can give us max 3 numbers
35n < 100 .... can give us max 2 numbers
55n < 100 .... can give us max 1 number
65n < 100 .... can give us max 1 number
85n < 100 .... can give us max 1 number
so Ans = 6+3+2+1+1+1 = 14
Please hit Kudos to encourage !!
Set A = {5n} where n = 1,2,3, .....
Set B = {3 , 5 , 7 , 11 , 13 , 17}
Now Set Z is just product of all element of A and B
(Note: Its product of a all possible combination in A and B. But we have defined only one element in A so problem has got much easy.
)So,
Set Z = {15n , 25n , 35n , 55n , 65n , 85n)
To satisfy condition of Z < 100
15n < 100 .... can give us max 6 numbers
25n < 100 .... can give us max 3 numbers
35n < 100 .... can give us max 2 numbers
55n < 100 .... can give us max 1 number
65n < 100 .... can give us max 1 number
85n < 100 .... can give us max 1 number
so Ans = 6+3+2+1+1+1 = 14
Ans B
Please hit Kudos to encourage !!
