Re: A certain customer at a health food store purchased organic bananas at
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15 Jul 2019, 11:16
A certain customer at a health food store purchased organic bananas at a price of $.70 each, and conventional bananas at a price of $.60 each. How many total bananas did the customer purchase, if he purchased both organic and conventional bananas?
Let O be number of organic bananas and C be number of conventional bananas.
We know that O and C are both positive integers because number of banans cannot be fractional or negative. Also, it is given that he purchased both, so they are not equal to 0.
Total amount = O*0.7 + C*0.6
We have to find O + C
(1) In total, the customer spent $5.60 on bananas
0.7*O + 0.6*C = 5.6
O has to be 7 or lower ....because if O was 8, total cost would be more than 5.6$ (minimum value of C is 1)
Similarly, C has to be 8 or lower... because if C was 9, total cost would be more than 5.6$ (minimum value of O is 1)
Possible values of O - 7,6,5,4,3,2,1
Possile values of C - 8,7,6,5,4,3,2,1
Lets try all possible values of O to see which combinations allow Total = 5.6
O ____C____ Total
7 ____1____ 5.5..... O=7 is not possible. If O is 7, C =1 is closest to bringning total to 5.6. No value of C will bring total to exactly 5.6.
6 ____2____ 5.4..... O=6 is not possible. If O is 6, C =2 is closest to bringning total to 5.6. No value of C will bring total to exactly 5.6.
5 ____3____ 5.3..... O=5 is not possible. If O is 5, C =3 is closest to bringning total to 5.6. No value of C will bring total to exactly 5.6.
4 ____4____ 5.2..... O=4 is not possible. If O is 4, C =4 is closest to bringning total to 5.6. No value of C will bring total to exactly 5.6.
3 ____5____ 5.1..... O=3 is not possible. If O is 3, C =5 is closest to bringning total to 5.6. No value of C will bring total to exactly 5.6.
2 ____7____ 5.6..... CORRECT
1 ____8____ 5.5..... O=1 is not possible. If O is 1, C =8 is closest to bringning total to 5.6. No value of C will bring total to exactly 5.6.
There is only 1 combination of positive integers that brings total to 5.6$
So O =2, and C = 7,
(1) IS SUFFICIENT
(2) The customer purchased conventional and organic bananas in the ratio of 7:2 respectively
C/O = 7/2
C and O could be 7 and 2 respectively
C and O could be 14 and 4 respectively
Cannot narrow down to 1 value
(2) IS NOT SUFFICIENT
ANSWER: A - (1) Alone is SUFFICIENT