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

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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, 12:56
1
From Question stem, we have, cost of Organic bananas = 0.7 and cost of Conventional bananas = 0.6. We have to find the total number of bananas purchased.

Stmt 1: Gives us the total amount spent on bananas is $5.60. That is, 0.7X + 0.6Y = 5.60, where X = # of organic bananas and Y = # of Conventional bananas.

Since the total amount is a small number, $5.60, we can quickly check different values of X and Y and we can see that total amount spent will be equal to $5.60 only when X = 2 and Y = 7.
Trying any other combination of X and Y will not give a total amount of $5.60.
Hence, sufficient.

Stmt 2: Gives us only the ration of the two types of bananas. So it could be that the customer bought 2 Organic bananas and 7 Conventional bananas, or 4 organic and 14 conventional and so on. Hence sufficient because we can tell for sure the total number of bananas purchased.

Correct answer thus 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, 12:57
1
Price per organic banana=0.7 and price per conventional banana=0.6. Let x and y represent organic and conventional bananas respectively, while t represent total bananas bought.
Total cost of bananas = 0.7x+0.6y
x+y=t
From statement 1: we know that 0.7x+0.6y=5.6
This also means 7x+6y=56
Now if we can find a combination of two non-zero integers for x and y such that 7x+6y=56, then t=x+y
Non zero because the question says categorically that the customer purchased both bananas.

A good place to look is to take a look at the the factors of 56 which are: {1,2,4,7,8,14,28,56}

From the set, when x=2, and y=7, we can tell that the total bananas bought equals 9, since 0.7(2)+0.6(7)=5.6

The only other option available is if the customer bought only organic bananas and no conventional bananas. But from the question, the customer bought both, hence we can disregard this possibility.

Statement 1 alone is sufficient.

Statement 2: x:y=7:2
This means that x=(7/9)*t
and y=(2/9)*t
This is clearly insufficient since the ratio x:y=7:2 can be expressed in many forms such as 14:4, 21:6, 28:8 with corresponding t equals 9,18,27,36. Hence statement 2 on its own is insufficient.

The correct answer therefore 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, 13:45
Lets take X as no of OB and Y as no of CB.
.70x +.60y=5.60

To prove x+y=?

From A
If you would see than only pair that would make 5.60 dollar is x=2 and y=7. 1.40+4.20=5.60.

From B
Ratio is just not enough. We need the amount of bananas.

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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, 13:52
Answer is D

Let Organic bananas = o, Price = 0.70 each
Conventional bananas = c, Price = 0.60 each
Customer bought both type of bananas.
Question is asking o+c=?

St.1 - o+c=5.60
=>0.7o+0.6c=5.6
=>7o+6c=56
since the total amount is $56, here only one combination works and that is the customer bought 7 conventional bananas and 2 organic bananas. Sufficient

St.2 - The ratio of conventional and organic bananas is 7:2. Therefore if we multiply the ratio with the price of each banana then we will get the total number of bananas the customer bought. Sufficient

Answer is D
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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, 15:36
1
Question: 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. SUFFICIENT
- The question states that both organic and conventional bananas were purchased, therefore neither quantity can be equal to zero.
- To make things easier, instead of working with .70, .60, or 5.60 change your values to whole numbers 7, 6, 56 respectively.
- Factors of 56 are as follows (1,2,4,7,8,14,28,56).
- 7 goes into four of 56's factors, (7, 14, 28, and 56).
- Organic quantities of (7, 14, 28, and 56) can be compared to multiples of Conventional.
- Any multiple of 6 that goes evenly into 56 after one of the four organic quantities (7, 14, 28, and 56), is correct.
\[
\begin{matrix}
Organic & + & Conventional & = & Total Cost &y = ? & Correct? & x+y \\
7x & + & 6y & = & 56 & & & \\
7(1) & + & 6y & = & 56 & y = 8.166 & Incorrect & \\
7(2) & + & 6y & = & 56 & y = 7 & Correct & 9\\
7(4) & + & 6y & = & 56 & y = 4.66 & Incorrect & \\
7(8) & + & 6y & = & 56 & y = 0 & Incorrect & \\
\end{matrix}
\]

(2) The customer purchased conventional and organic bananas in the ratio of 7:2 respectively. INSUFFICIENT
- Ratio multiples create multiple answer possibilities.
\[
\begin{matrix}
Ratio & Organic & + & Conventional & = & Total \\
y:x & 7x & + & 6y & = & x + y \\
7:2 & 7(2) & + & 6(7) & = & 9&\\
14:4 & 7(4) & + & 6(14) & = & 18\\
21:6 & 7(6) & + & 6(21) & = & 27\\
\end{matrix}
\]

Correct 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, 16:10
1
We have been given the prices of the two types of bananas: PO=0.70 and PC= 0.60 and are asked to calculate the total number of bananas purchased, or \(o+c=?\)

(1) In total, the customer spent $5.60 on bananas: We now know the price of each type of banana as well as the total money spent on both bananas. This would give us an equation with two variables, i.e. \(0.7o + 0.6c = 5.6\) ==>> \(7o+6c=56\) ==>> \(c=\frac{(56-7o)}{6}\).

Now because we are dealing with bananas, the solution to the above equation has to be in the form of integers and looking at the form of the simplified equation where C is the subject, we know that any value of o should be such that (56-7*o) should be a multiple of 6. We can also deduce from this equation that o<7 as o=8 will give us a value of zero for c and we've been told in the question that the customer buys both types of bananas. Cycling through possible values of o that give you integer values of c, you will realize that only o=2 and c=7 satisfies this equation. Total bananas=c+o=7+2=9 Thus A is sufficient.

(2) The customer purchased conventional and organic bananas in the ratio of 7:2 respectively - This can give you an infinite number of values of both o and c and therefore o+c. e.g. if o=2 c=7 and o+c=9, if o=4; c=14 o+c=18, if o=6 c= 21 o+c=27 and so on. Note that given the ratio of c:o=7:2, only even values of o will be possible as both c and o need to be integers. Even so as more than one value of c+o is possible, statement 2 is insufficient.

Answer is therefore 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, 17:02
1
multiply all by 10
O-7 ,C-6
CASE 1)total 56--
including both 7 and 6
only one possibility
7*2 + 6*7
sufficient

case 2)
possibilities
7,2
14,4.............
not sufficient

Therefore, 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, 17:04
1
A says total is 5.6
x = organic bananas and y= conventional bananas
Hence equation becomes 0.7x+0.6y=5.6
which gives unique solutio of X=6 Andy=2
X=8 and y=0 is not possible as he purchased both bananas as per Question
Hence A is sufficient

B only states the ratio which is insufficient to answer the question as there is no unique answer

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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, 17:05
1
Let o = number of organic bananas and c= number of conventional bananas
Therefore, 0.7o+0.6c = total spent
The question asked us for o+c=?

St 1: 0.7o+0.6c=5.6 ==> 10 x \((\frac{7o}{10}+\frac{6c}{10}=\frac{56}{10})\) ==> 7o+6c=56

Therefore, o = \(\frac{56-6c}{7}\)==> 8 - \(\frac{6c}{7}\) ==> c is a multiple of 7 since 6 is not divisible by 7 (i.e, since o and c have to be integers)

Say c = 7 ==> o = 8 - \(\frac{(6 × 7)}{7}\) = 8 - 6 = 2 ==> o+c = 2+7 = 9 ==> St 1 is sufficient

Note: o cannot be zero (i.e, c = 8) because we are told that the customer bought both types of banana

St 2: \(\frac{c}{o}\) = \(\frac{7}{2}\) ==> o+c is a multiple of 9 (i.e, 9, 18, 27, 36, 45, 54, ...) ==> St 2 is not sufficient.

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, 17:52
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

Number of organic bananas = A
Price of organic bananas = $.7
Number of conventional bananas= B
Price of conventional bananas = $.6

customer bought both type of bananas so total bananas bought by customer = A+B


As per option, total money spent by customer on bananas is $5.6

=> .7A + .6B = 5.6
=> 7A + 6B =56
=> 6B= 56-7A
=> 2*3= 56-7A
=> Pls notice that coefficient of A is prime number and coefficient of B is even number so if we arrange equation, 56-7A should be even number and should be divisible by both 2 & 3. Only A=2 satisfies required condition.

So statement 1st is sufficient.

Let's consider statement 2nd.

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

=> .7A+.6B = 7x+2y it can be anything. so statement 2nd is not sufficient.

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, 19:02
For (1), let's make the number of organic bananas x, and the number of conventional bananas y. So now we get 0.7x+9.6y=5.6. And we still don't know x and y, so (1) is insufficient

For (2), we know the ratio is 7:2, which means y/x=7/2, and we get 2y=7x, y=7x/2. But we still don't know x and y, so (2) is insufficient.

Combine (1) and (2), now we know y=7x/2, which mean 0.7x+0.9(7x/2)=5.6, so we could get the answer of x. Finally, with the answer of x, by using the formular y=7x/2, we could get the answer for y

So choose C.
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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, 19:06
1
X = Organic bananas ; price = 0.70 each
Y = Conventional bananas ; price = 0.60 each

What is X + Y?
X, Y >=1

(1) In total, the customer spent $5.60 on bananas
0.70X + 0.60Y = 5.60 ;
70X+60Y=560;
7X+6Y=56
Try number picking ; There is only one combination of X = 2, Y = 7 that will result in 56 . hence, sufficient.

(2) The customer purchased conventional and organic bananas in the ratio of 7:2 respectively
\(\frac{X}{Y}\) = \(\frac{2}{7}\) so total number of bananas is multiple of 9, it could be 9, 18, 27, ... hence, not sufficient.

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, 20:13
As the person bought both bananas , only 2: 7 will fit this equation. We can substitute and see that no other values fit the equation .70x + .6y = 5.60
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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, 20:13
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

let organic bananas be x
and inorganic be y
1) 0.7x+0.6y = 5.60
So s per equation
7x+6y = 56
now x and y can only be integers
the values x and y satisfy are
(x,y) = (4,8)
Also given both organic and inorganic were purchased hence x or y cant be zero
Hence sufficient

2) As per given y:x = 7:2
= 7k and 2k
total cost = 2*0.7 k +7*0.6k
1.4k+4.2k = 5.6k
now k can be 10, 100 or even a number such as 4, 5
hence no unique answer
thus not sufficient

Thus 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, 20:24
A has to be the right answer because of the only possible ratio of 7:2.
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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, 20:48
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

Solution:
Let the number of conventional bananas bought be a
and the number of organic bananas bought be b

Considering statement (1) alone:
0.7b + 0.6a = 5.6
As a and b have to be integers, there is only one set of values that work this.
a = 7 and b = 2
SUFFICIENT

Considering statement (2) alone:
a/b = 7/2
There could be many possible values for a and b now.
INSUFFICIENT

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, 21:15
1
Organic Banana (B) costs $0.70
Conventional banana(C) costs $.60
At least one of each type was bought by customer

(1) In total, the customer spent $5.60 on bananas, ---> 0.7B+0.6C=5.6 => 7B+6C=56, 6C is always even, since the sum of &B and 6C is even, 7B must also be even, Lets check for B=2,4,6,8
At B=2, C=7-->Possible,
At B=4, C is not integer --->Not possible
At B =6, C is not integer --->Not possible
At B=8, C is 0----> Violates given condition
Hence, B=2, C=7 is the only possible solution. Sufficient.

(2) The customer purchased conventional and organic bananas in the ratio of 7:2 respectively
C=7, B=2 Possible
C=14, B=4 Also Possible,
Many solutions exist. --->Clearly insufficient.

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, 21:20
1
Let customer purchased x organic banana and y conventional bananans,
.7x+.6y= Amount spend

1) 7x+6y=56
Since x and y have to be positive integers. for x=2 and y=7, this is sufficient.

2) y/x = 7/2 => y=7x/2
2.8x = Amount spend. Not sufficient.


Hence option A IMO.
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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, 21:29
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?

Consider,
Conventional banana:x
Organic banana: y
x or y cannot be 0.

(1) In total, the customer spent $5.60 on bananas
We can form equation
0.6 x + 0.7 y = 5.6
If we put different values in x and y then we get y can be 2 and x can be 7.
So we can say customer purchased total 9 bananas.
Sufficient.

(2) The customer purchased conventional and organic bananas in the ratio of 7:2 respectively
We can write this as
7 x / 2 y
But we dont know that how much bananas customer purchased. It can be 9 or 18 or... so on.
There is no limiting factor.
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, 21:42
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

Here, only possible combination is 7 conventional and 2 organic bananas(0.6*7+0.7*2=5.6). (customer purchased both types of bananas)
So, '1' can answer the question.

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

Given information is not enough. Total bananas can be anything from [9, 18, 27, .....]
So, '2' can not answer the question.


ANSWER: A
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Re: A certain customer at a health food store purchased organic bananas at   [#permalink] 15 Jul 2019, 21:42

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