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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, 21:52
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

Let, organic banana = x and conventional banana = y
So, total spent = 0.70x + 0.60y
Stmt 1: 0.70x + 0.60y =5.60
it can be solved only when x=2 and y =7. so, sufficient. Eliminate B, C and E.

Stmt 2: it provides only the ratio of the number of banana in which the value of x and y can be anything. so, insufficient.

so, the correct answer choice 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, 22:25
2
In the first statement it is given that the 5.60 is total amount paid by the consumer. By converting it into algebraic form we get x +y= 1.30 the second expression is 0.70x+0.60y=5.60. by solving this we get an answer. in statement 2 the ratios are given so can't substitute the values in it. Hence selected A as statement 1 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, 23:51
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?


Given price of each Organic banana = 0.70, no of organic bananas = x
price of each regular banana = 0.60, no of regular bananas = y


===> Total money spent = x*0.70 + y*0.60

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

Given total money spent = 5.60 = x*0.70 + y*0.60
=> 56 = 7x+6y
Even though it is a equation with 2 unknows , we can find the solution with try and error as only solutions fits is x = 2 , y =7


(2) The customer purchased conventional and organic bananas in the ratio of 7:2 respectively-Not Sufficient

Given \(\frac{x}{y}=\frac{7}{2}\)
==> x = 7,14,21
==> y = 2,4,6
So not sufficient

Option A is the correct 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 16 Jul 2019, 00:31
1
As per me, answer should be A, because B gives just ratio but no numerical number/variable. At the same time A gives us algebraic equation with with we can arrive to exact numbers. 0.70a+0.60b=5.60 (I tested all numbers from 1 to 8 and only 2 and 7 work) 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 16 Jul 2019, 01:10
Let the number of organic bananas = x &
number of conventional bananas = y

To Find: "x + y"
Note: Neither x nor y can take value = 0

(1) In total, the customer spent $5.60 on bananas
--> 0.7x + 0.6y = 5.6
--> 7x + 6y = 56

'x' has to take only even values [Since \(y = \frac{(56 - 7x)}{6}\)]
--> If x = 2, y = 7 - Possible
x = 4, y = 14/3 - Not Possible
x = 6, y = 7/3 - Not Possible

Sufficient

(2) The customer purchased conventional and organic bananas in the ratio of 7:2 respectively
--> y = 7k, x = 2k ; for any positive integer k
--> 7(2k) + 6(7k) = 56
--> 14k + 42k = 56
--> 56k = 56
--> k = 1

--> x = 2, y = 7

Sufficient

IMO Option D

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

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New post 16 Jul 2019, 03:21
1
First statement alone is sufficient because stem told us that each kind of banana was purchased (thus we are dealing with positive integers) and that .7x+.6y=5.6. Only integers 2 and 7 will yield 5.6 dollars. Other will have to be either decimals or 0 for (y). Cross BCE.
Second statement alone is not sufficient because we are given just a ratio. The total number can be 9 or 90 or 900 or anything else that is a multiple of 9 (7 conventional and 2 organic bananas). Cross D.
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 16 Jul 2019, 03:35
1
It is A

(1) In total, the customer spent $5.60 on bananas - - in order to simplify, we will round 0.60 to 6, and 0.70 to 7, and 5.6 to 56. So customer purchased 6x+7y=56. If x=0, y=8 but x cannot be 0. If x=1, y is not integer. If x=2, y=7. If x=3, y=not integer.... until x=9, y is not integer. Statement 1 is sufficient because we got exact number (2 and 7, total number of bananas)
(2) The customer purchased conventional and organic bananas in the ratio of 7:2 respectively - customer purchased 9x bananas. No way to find x, B 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 16 Jul 2019, 04:02
A.

St. 1 is sufficient- just plug in different numbers, you'll get a unique combination that suits the total value.

Ans- 9 bananas (2 organic & 7 conventional).
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Re: A certain customer at a health food store purchased organic bananas at  [#permalink]

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New post 16 Jul 2019, 04:02
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

STATEMENT (1): Let the number of organic bananas be x and the number of conventional bananas be y

We have 0.70x + 0.60y = 5.60

Since x and y both need to have integral values (since the number of bananas can't be in fractions), only 1 set of values, i.e. x = 2 and y = 7 satisfy this equation. Hence, the total number of bananas purchased = x + y = 2 + 7 = 9.

Statement (1) is SUFFICIENT.


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

Statement (2), we only have the ratio of bananas and nothing else except the costs of each type of bananas, there's no way we can find the number of bananas, and HENCE, this statement is CLEARLY INSUFFICIENT.

Thus, (A) is the correct answer choice.
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Re: A certain customer at a health food store purchased organic bananas at  [#permalink]

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New post 16 Jul 2019, 05:26
2
Let the number of organic bananas bought be o and that of conventional bananas be c
We need to find the value of (o+c).
It is also given that \(o,c\geq{1}\)

Statement 1:
0.7o+0.6c = 5.6
At first, we may think that this info is not sufficient.
However, let us substitute different values of o and c to satisfy this eqn (given that \(o,c\geq{1}\))

As 0.6c results in a number with an even tenth digit for any integral value of c, 0.7o should have an even tenth digit as the RHS (5.6) has an even tenth digit. So, o should have only even values to satisfy the equation. Just think about it!

o=2, c=0.42/.6=7; We get an integral value for c. Hence, this is a possible case.
o=4, c=0.28/.6; \(c\neq{Integer}\). Hence, not possible.
o=6, c=0.14/.6; \(c\neq{Integer}\). Hence, not possible.
o=8, c=0/.6=0; But we know that \(c\geq{1}\). Hence, not possible.
Higher values of o give negative values of c which are not possible.

Hence, the only possible solution is o=2, c=7. Therefore, o+c=9.
Statement 1 is sufficient.

Statement 2: \(\frac{c}{o}=\frac{7}{2}\)
We can't find the value of o+c just by knowing the ratio o:c.
Statement 2 is insufficient.

Hence, option (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 16 Jul 2019, 05:27
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

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

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 16 Jul 2019, 05:47
1
lets say we have x organic bananas
and y conventional bananas

Stment 1 =
(1) In total, the customer spent $5.60 on bananas
0.7x+0.6y = 5.60

Here we have a unique scenario for x value of 2 and Y value of 7.

So this statement is sufficient .


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

This statement is not sufficient since in this given ratio we will not be having any fixed count of bananas

So 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 16 Jul 2019, 06:28
1
IMO the answer should be A as there is just one possibility which is 2(0.70)+7(0.60)

In case of B there is a ratio 7:2, but we cannot find a specific number.
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Re: A certain customer at a health food store purchased organic bananas at  [#permalink]

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New post 16 Jul 2019, 06:49
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The price of Organic bananas - $0.7 each
The price of Conventional bananas - $0.6 each

And The customer purchased at least one banana from both types of bananas

Statement1: in Total, The customer spent $5.6 on bananas
The equation will be 0.7x+0.6y=5.6

(x- the number of Organic bananas
y-the number of Conventional bananas)

In order to find the total bananas, we need the ratio of x and y:
if
x=1, 0.6y=5.6-0.7=4.9
y=4.9/0.6 (y cannot be integer, y should be integer)
x=2, 0.6y=5.6-1.4=4.2
y=7 (integer, we'll keep it).
We have to check the all possibility, because if two answers satisfies, statement will be insufficient)
x=3, 0.6y=5.6-2.1=3.5 (y cannot be a integer)
x=4, 0.6y=5.6-2.8=2.8 (y cannot be a integer)
x=5, 0.6y=5.6-3.5=2.1 (y cannot be a integer)
x=6, 0.6y=5.6-4.2=1.4 (y cannot be a integer)
Yes, we have just one ratio of x and y that will satisfies the equation. 2 organic bananas and 7 conventional bananas.
Sufficient.

Statement2:
Conventional / organic bananas = 7 : 2 respectively
Given ratio of two types bananas is good, but we don't have a total amount expenses on bananas.
That's why, The total number purchased bananas could be:
7+2 =9
14+4=18
21+6=27 and so on...
Insufficient

The Answer choice 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 16 Jul 2019, 07:28
2
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
Customer purchased both kinds of bananas a (organic) and b (conventional) and positive integers, we can consider:
0.7a + 0.6b = 5.6
By guessing possible numbers, we can get that 2 (a-organic) and 7 (b-conventional)
This condition makes A sufficient for us.


(2) The customer purchased conventional and organic bananas in the ratio of 7:2 respectively
Could be a lot of different situations, so the customer could buy:
7a+2b = 9 (a=1, b=1)
7a+2b=18 (a=2, b=2)
7a+2b=27 (a=3, b=3)
7a+2b=36 (a=4, b=4) etc...
So this condition is not sufficient to find exact quantity bought bananas.

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

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New post 17 Jul 2019, 04:30
someneha wrote:
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?


No. of Organic Bananas = x => Costs 0.70/piece
No. of Conventional Bananas = y => Costs 0.60/piece

We need to find (x+y)

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


0.70x + 0.60y = 5.60
70x+60y=560
7x+6y=56

Insufficient.

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


x=2a
y=7a
x+y = 9a

Insufficient.

Let's combine statements (1) & (2),

7x+6y=56
7(2a)+6(7a)=56 (At this step, we can be sure that we can solve the equation for a and find an answer.)
14a+42a=56
56a=56
a=1
So, x+y=9.

Sufficient.

Hence Ans should be (C)



Hi Bunuel,

I thought 2 variables, 1 equation. So, it's not enough.

When are we supposed to try to find the value of an equation by trial and error? Always?
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Re: A certain customer at a health food store purchased organic bananas at  [#permalink]

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New post 17 Jul 2019, 06:07
1
someneha I am not Bunuel, but I can help. We solved this question this way because of the limitations in the problem and the equation (7O+6B=56) restrict the values the variables involved can take, so it doesn't happen everything. Hope this helped.
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Re: A certain customer at a health food store purchased organic bananas at  [#permalink]

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New post 24 Jul 2019, 23:39
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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Re: A certain customer at a health food store purchased organic bananas at   [#permalink] 24 Jul 2019, 23:39

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