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20 Jul 2022, 01:30
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\(A = {3, 9, 10, 15}\)
\(B = {5, 12, 15, 21}\)
x is one of the elements in set A, and y is one of the elements in set B. What is the value of x + y ?
(1) Exactly one of x and y is odd.
(2) Exactly one of x and y is prime.
Are You Up For the Challenge: 700 Level Questions
\(B = {5, 12, 15, 21}\)
x is one of the elements in set A, and y is one of the elements in set B. What is the value of x + y ?
(1) Exactly one of x and y is odd.
(2) Exactly one of x and y is prime.
Are You Up For the Challenge: 700 Level Questions
20 Jul 2022, 05:35
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A typical question where we need to consider different scenarios.
A=3,9,10,15
B=5,12,15,21
Statement 1
Exactly one of x and y is odd.
Not sufficient as we have 5 possibilities.
Statement 2
Exactly one of x and y is prime.
Again not sufficient.
Now we combine.
Now only option that is common between the two is 15. So we can get the answer after the combination.
And also we can now start with statement 2 as it gives limited cases for us.
If x = 3, y = 12
If y = 5, x = 10
Although we have 2 scenarios, both give the same 15 as the answer. Hence the answer is 'C'.
Note
When in a question they ask about sum or product of some numbers, always be vigilant about the fact that multiple scenarios can lead to the same answer.
A=3,9,10,15
B=5,12,15,21
- x is one of the elements in set A, and y is one of the elements in set B. We need to find "x + y"
Statement 1
Exactly one of x and y is odd.
- So we can have either x is odd and y even or vice versa.
Scenario 1: x = 3/9/15 and y = 12
Scenario 2: x = 10, y = 5/15/21
- Since we are looking for possible sums so those can be 15, 21, 27, 15 (repeat), 25, 31
Not sufficient as we have 5 possibilities.
Statement 2
Exactly one of x and y is prime.
- Here also x can be prime and y composite or vice versa.
Scenario 1: x = 3, y = 12/15/21
Sceanrio 2: y = 5, x = 9/10/15
The sum can be 15, 18, 24, 14, 15 (repeat), 20
Again not sufficient.
Now we combine.
Now only option that is common between the two is 15. So we can get the answer after the combination.
And also we can now start with statement 2 as it gives limited cases for us.
If x = 3, y = 12
If y = 5, x = 10
Although we have 2 scenarios, both give the same 15 as the answer. Hence the answer is 'C'.
Note
When in a question they ask about sum or product of some numbers, always be vigilant about the fact that multiple scenarios can lead to the same answer.
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