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What is the price of an orange?
(1) The price of 3 oranges and 2 apples is $7.
(2) The price of an orange and the price of an apple are both integers.
(1) The price of 3 oranges and 2 apples is $7.
(2) The price of an orange and the price of an apple are both integers.
18 Jun 2022, 23:26
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Let price of orange be x and price of apple be y. We need to find a unique value of x.
(1) The price of 3 oranges and 2 apples is $7.
=> 3x + 2y = 7
If we plot graph for this line, we see there are multiple possible values for x and y. This is because we don't know whether the values of x and y is an Integer.
e.g., if x = 1 then y = 2 and if x = 2 then y = 1/2. And, both these values are valid.
Statement 1 is insufficient.
(2) The price of an orange and the price of an apple are both integers.
=> This is clearly insufficient, as we can infinite possible integers.
Combining (1) and (2) we get,
3x+2y = 7 and values of x and y are integers
There is only one possible value x=1 and y=2.
( To find other integral solutions we need to decrease and increase the identified integer solution of x and y by the coefficients of y and x respectively.
a. If we reduce one '2' from x=1 and increase one '3' from y=2 we get another integer solution for 3x+2y = 7 i.e., x=-1 and y=5. But value of x cannot be negative.
b. Similarly, if we increase one '2' from x=1 and decrease one '3' from y=2 we get another integer solution for 3x+2y = 7 i.e., x=3 and y=-1. But value of y cannot be negative.
Thereby, all integer solutions of x and y, other than x=1 and y=2, will have either x or y as a negative value.)
Answer: C
(1) The price of 3 oranges and 2 apples is $7.
=> 3x + 2y = 7
If we plot graph for this line, we see there are multiple possible values for x and y. This is because we don't know whether the values of x and y is an Integer.
e.g., if x = 1 then y = 2 and if x = 2 then y = 1/2. And, both these values are valid.
Statement 1 is insufficient.
(2) The price of an orange and the price of an apple are both integers.
=> This is clearly insufficient, as we can infinite possible integers.
Combining (1) and (2) we get,
3x+2y = 7 and values of x and y are integers
There is only one possible value x=1 and y=2.
( To find other integral solutions we need to decrease and increase the identified integer solution of x and y by the coefficients of y and x respectively.
a. If we reduce one '2' from x=1 and increase one '3' from y=2 we get another integer solution for 3x+2y = 7 i.e., x=-1 and y=5. But value of x cannot be negative.
b. Similarly, if we increase one '2' from x=1 and decrease one '3' from y=2 we get another integer solution for 3x+2y = 7 i.e., x=3 and y=-1. But value of y cannot be negative.
Thereby, all integer solutions of x and y, other than x=1 and y=2, will have either x or y as a negative value.)
Answer: C
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