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A certain customer at a health food store purchased organic bananas at

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A certain customer at a health food store purchased organic bananas at  [#permalink]

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New post 15 Jul 2019, 08:00
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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?

(1) In total, the customer spent $5.60 on bananas
(2) The customer purchased conventional and organic bananas in the ratio of 7:2 respectively

 

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Re: A certain customer at a health food store purchased organic bananas at  [#permalink]

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New post 15 Jul 2019, 08:09
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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?

Before moving to answer choices analyze the question.
Let Organic be x and conventional be y.
The equation is 70x + 60y

(1) In total, the customer spent $5.60 on bananas
Using this statement we have 70x + 60y = 560, only 1 solution is possible 2 of conventional and 7 of organic. Hence this is sufficient.


(2) The customer purchased conventional and organic bananas in the ratio of 7:2 respectively
This is clearly insufficient as it could be 7 & 2 or 14 & 4.

Hence the answer is A.
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Re: A certain customer at a health food store purchased organic bananas at  [#permalink]

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New post 15 Jul 2019, 08:08
1
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?

(1) In total, the customer spent $5.60 on bananas
(2) The customer purchased conventional and organic bananas in the ratio of 7:2 respectively

Option 1 says customer spent $5.6 and in question we are told customer purchases both type of bananas. The only combination which satisfy the total bill of $5.6 is 2 organic bananas and 7 conventional bananas. - Sufficient

Option 2 tells us customer purchases in ratio of 7:2. but we can't tell total number of bananas based on it - Insufficient

Answer : A
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Re: A certain customer at a health food store purchased organic bananas at  [#permalink]

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New post 15 Jul 2019, 08:09
Answer is B. Statement 2 is sufficient.
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Re: A certain customer at a health food store purchased organic bananas at  [#permalink]

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New post 15 Jul 2019, 08:09
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IMO answer is A

let the customer by x organic and y conventional bananas
from1: 0.7x+0.6y = 5.6, only integers that satisfy this equation is x= 2, y = 7, so sufficient

from 2: the customer could have purchased 7 conventional and 2 organic, or 14 conventional and 4 organic bananas, giving different answers so not suff

so Answer is A
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Re: A certain customer at a health food store purchased organic bananas at  [#permalink]

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New post 15 Jul 2019, 08:10
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Let no. of organic bananas be x and no. of conventional bananas be y
0.7x +0.6y = 5.6 --- statement 1 (insufficient) 2 solutions possibles x=2, y=7 & x=8, y=0

y/x = 7/2 --- statement 2 (alone insufficient)

Together sufficient ( 2 variables, 2 equations)
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Re: A certain customer at a health food store purchased organic bananas at  [#permalink]

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New post 15 Jul 2019, 08:13
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(1) In total, the customer spent $5.60 on bananas

Let the no of organic bananas be x and no of conventional bananas be y.

0.7x + 0.6y = 5.6

7x + 6y = 56

The only combination which would satisfy this condition is when x =2 and y=7

Hence sufficient.

(2) The customer purchased conventional and organic bananas in the ratio of 7:2 respectively

We do not know the exact no of bananas.

Hence insufficient.

Answer should be A.
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A certain customer at a health food store purchased organic bananas at  [#permalink]

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New post 15 Jul 2019, 08:13
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Let the number of organic bananas be a and the number of conventional bananas be b where a and b are positive integers since it is given that the customer purchased both

(1) In total, the customer spent $5.60 on bananas

0.7a + 0.6b = 5.6 or,
7a + 6b = 56

Since we know that both a and b are integers greater than 0, we can deduce that the above equation holds true only when a=2 and b=7. So the total number of bananas that the customer bought is 9

Sufficient

(2) The customer purchased conventional and organic bananas in the ratio of 7:2 respectively

The customer could have bought
7 organic bananas and 2 conventional bananas, or
14 organic bananas and 4 conventional bananas, and so on

Insufficient

Answer is (A)
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A certain customer at a health food store purchased organic bananas at  [#permalink]

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New post Updated on: 16 Jul 2019, 06:20
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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?

(1) In total, the customer spent $5.60 on bananas
(2) The customer purchased conventional and organic bananas in the ratio of 7:2 respectively

Given: 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
Asked: How many total bananas did the customer purchase, if he purchased both organic and conventional bananas?

(1) In total, the customer spent $5.60 on bananas
.7x + .6y = 5.6
7x + 6y = 56
\(x = \frac{56-6y}{7}\)
and x & y are both integers
(56/7,0), (50/7,1), (44/7,2), (38/7,3), (32/7,4),(26/7,5), (20/7,6), (14/7=2,7), (8/7,8), (2/7,9) are possible solution but x&y need to be integers
It gives x = 2 & y=7 (2,7) as the only solution
Total bananas = x+y = 2+7=9
SUFFICIENT

(2) The customer purchased conventional and organic bananas in the ratio of 7:2 respectively
Let us assume that conventional bananas purchased = 7x & organic bananas purchased = 2x
7x *.6 + 2x * .7 = total amount spent
Since any $ amount is not mentioned, value of x can not be derived.
e.g 7 + 2 =9 is valid
But 14 + 4 =18 is also valid
NOT SUFFICIENT

IMO A
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Originally posted by Kinshook on 15 Jul 2019, 08:15.
Last edited by Kinshook on 16 Jul 2019, 06:20, edited 2 times in total.
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Re: A certain customer at a health food store purchased organic bananas at  [#permalink]

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New post 15 Jul 2019, 08:16
1
Quote:
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?


To sum up, we have the following conditions:
Conventional Bananas (x) = $0.6
Organic Bananas (y) = $0.7
Both x and y were purchased.
We need to find out the value of x + y (total number of bananas bought)

Let us analyze statements.

Statement 1:
(1) In total, the customer spent $5.60 on bananas

Based on this statement, we can conclude that 0.6x + 0.7y = 5.6
We also know that at least 1 banana of each type was bought. It can be observed that the only integers x and y that can be used in this equation, are x = 7 and y = 2.
Other values of x and y will not end up in obtaining the final cost of bananas equal to $5.6. Thus, the statement 1 is sufficient.
Sufficient.

Statement 2:
(2) The customer purchased conventional and organic bananas in the ratio of 7:2 respectively

From this statement, x : y = 7 : 2. However, we do not know what are the exact values of x and y. It can be 7 : 2 or 21: 6, and the ratio will still be 7 : 2. Thus, this information is insufficient.
Insufficient.

Conclusion: Statement 1 alone is sufficient to give a correct answer.

Answer: A
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Re: A certain customer at a health food store purchased organic bananas at  [#permalink]

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New post 15 Jul 2019, 08:19
1
from given info
.7x+.6y total cost
and x+y total bananas
#1
.7x+.6y=5.6
only possible when x=2 and y=7
so total bananas; 9 sufficient
#2
The customer purchased conventional and organic bananas in the ratio of 7:2 respectively
so total bananas can be either 9 , 18 , 27 .... so on in sufficient
IMO A


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?

(1) In total, the customer spent $5.60 on bananas
(2) The customer purchased conventional and organic bananas in the ratio of 7:2 respectively
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Re: A certain customer at a health food store purchased organic bananas at  [#permalink]

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New post 15 Jul 2019, 08:30
1) the first sentence tells that in total the customer bought bananas worth $5.6. if he bought both the bananas there could only be a pair of integers which can make up the total as $5.6 7,2 . So it's sufficient.

2) when you write the equation of the ratio and price

0.6*7x+0.7*2Y= Z

We do not know the total so it's not sufficient.

So A is the answer

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Re: A certain customer at a health food store purchased organic bananas at  [#permalink]

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New post 15 Jul 2019, 08:30
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Key take away from the question stem : OB- $.70 each, CB $.60 each. He purchased both

(1) In total, the customer spent $5.60 on bananas - Only one integer value set available 7 CB @ 4.2 and 2 OB @1.4 - Sufficient. 0 CB and 8 OB Not possible as it is clearly mentioned in the stem that he purchased both
(2) The customer purchased conventional and organic bananas in the ratio of 7:2 respectively - Ratio given but total cost. He can buy 7 CB and 2 OB or 14 CB and 4 OB. Insufficient

IMO A
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Re: A certain customer at a health food store purchased organic bananas at  [#permalink]

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New post 15 Jul 2019, 08:31
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(1) In total, the customer spent $5.60 on bananas
Since he bought at least 1 of each kind of bananas, the number of organic bananas should be even.
Let's check all cases.
Case 1.
0.7*2=1.4
5.6-1.4=4.2
4.2/0.6=7
Ok.

Case 2. 0.7*4=2.8
5.6-2.8=2.8
2.8/0.6 - cannot be devided

case 3.
0.7*6=4.2
5.6-4.2=1.4
1.4/0.6 cannot be devided

Thus we have only one solution and this statement is sufficient.


(2) The customer purchased conventional and organic bananas in the ratio of 7:2 respectively
Clearly not sufficient/

IMO A
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Re: A certain customer at a health food store purchased organic bananas at  [#permalink]

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New post 15 Jul 2019, 08:32
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A

Assuming the total number of conventional and organic bananas purchased are C and O, respectively.

Using st#1 and info given, we will get: 5.6 = 0.6C + 0.7O or 56 = 6C + 7O. Now, obviously both C and O are integers. Try all possible integer solutions of the equation, only C=7 and O=2 satisfies. Sufficient

Using st#2 and info given, we will get C/O = 7/2, and we have individual prices of each type of banana. Not sufficient
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Re: A certain customer at a health food store purchased organic bananas at  [#permalink]

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New post 15 Jul 2019, 08:34
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organic bananas=x->Total cost of organic bananas =0.7x
conventional bananas=y-> Total cost of conventional bananas=0.6y
Find x+y?

(1) In total, the customer spent $5.60 on bananas

0.7x+0.6y=5.6

Now only x=2 and y=7 (integral values) satisfies this equation
so, x+y=9
Sufficient

(2) The customer purchased conventional and organic bananas in the ratio of 7:2 respectively
Ratio is given, but multiplier of ratio could be 1,2,3...so on.
Insufficient

Hence A
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Re: A certain customer at a health food store purchased organic bananas at  [#permalink]

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New post 15 Jul 2019, 08:37
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IMO A.

Given: Organic bananas are sold at 0.7 each and conventional bananas at a price of 0.60 each.
The customer has bought a banana in each of the categories.

Statement 1: In total, the customer spent $5.60 on bananas.
We can write the equation as 0.7x + 0.6y = 5.60 where x represents the Organic bananas and y the conventional.
Multiplying by 10 both sides we get - 7x+6y =56.
We know that x,y>=1 and are integers.
Substituting values for y=1,2,3...we get values for x. The only values which satisfy this equation are x=2 and y=7.
Hence, this statement alone is sufficient.

Statement 2: The customer purchased conventional and organic bananas in the ratio of 7:2 respectively.
From this we get to know the equation would look like - 2x+7y. But we do not know how much the customer spent hence we cannot solve this equation.
Hence, this statement alone is not sufficient.
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Re: A certain customer at a health food store purchased organic bananas at  [#permalink]

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New post 15 Jul 2019, 08:37
1
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?

(1) In total, the customer spent $5.60 on bananas
(2) The customer purchased conventional and organic bananas in the ratio of 7:2 respectively

Statement 1 :-

0.70 x + 0.60y = 5.60.
This is possible only if x =2 and y=7
x & y should be integer.

\(x = (5.6-0.6y)/0.70\)

Try various values of v to get integer values of x.

When y= 7, \(x = (5.6-(0.6*7))/0.7\). x = 1.4/0.7 = 2.

Sufficient.

Statement 2 :-

The customer purchased conventional and organic bananas in the ratio of 7:2 respectively.

This is just a ratio. but there is no other clue. It can be multiples of 7:2 such as 14:4 or 28:8...
Not Sufficient.

Ans - A
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Re: A certain customer at a health food store purchased organic bananas at  [#permalink]

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New post 15 Jul 2019, 08:39
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Let organic banana price count --> a
conventional banana count --> b

From A
7a+6b=56

2 Solution set
(8,0) and (2,7)
From the main statement, Customer purchased both types of bananas.
So only one option remains

2 organic banana and 7 conventional banana

A is sufficient

B - it provides the ratio (7:2)
The ratio will point to multiple solutions
(7:2) , (14:4), (21:6).... so on
B is insufficient.

Hence, A is the answer.
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Re: A certain customer at a health food store purchased organic bananas at  [#permalink]

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New post 15 Jul 2019, 08:39
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(1) In total, the customer spent $5.60 on bananas - since the customer purchased both kinds of bananas, x (organic) and y (conventional) are positive integers. Algebraically, we get
70x+60y=560 (divide by 10)
7x+6y=56
Only integers 2 (for x - organic) and 7 (for y - conventional) work.
This makes A sufficient.

(2) The customer purchased conventional and organic bananas in the ratio of 7:2 respectively, - not sufficient. Could be 9 (7+2), 18 (14:4), etc
Answer is A
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Re: A certain customer at a health food store purchased organic bananas at   [#permalink] 15 Jul 2019, 08:39

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