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A certain customer at a health food store purchased organic bananas at
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15 Jul 2019, 08:00
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55% (01:51) correct 45% (01:52) wrong based on 310 sessions
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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
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15 Jul 2019, 08:09
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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15 Jul 2019, 08:08
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
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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
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15 Jul 2019, 08:09
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
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15 Jul 2019, 08:10
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
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15 Jul 2019, 08:13
(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
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15 Jul 2019, 08:13
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
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Updated on: 16 Jul 2019, 06:20
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 \(x = \frac{566y}{7}\) 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
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15 Jul 2019, 08:16
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 = 5.6We 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
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15 Jul 2019, 08:19
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
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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
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15 Jul 2019, 08:30
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. InsufficientIMO A
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Re: A certain customer at a health food store purchased organic bananas at
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15 Jul 2019, 08:31
(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 5.61.4=4.2 4.2/0.6=7 Ok.
Case 2. 0.7*4=2.8 5.62.8=2.8 2.8/0.6  cannot be devided
case 3. 0.7*6=4.2 5.64.2=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
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15 Jul 2019, 08:32
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
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15 Jul 2019, 08:34
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
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15 Jul 2019, 08:37
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
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15 Jul 2019, 08:37
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. \(x = (5.60.6y)/0.70\) 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
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15 Jul 2019, 08:39
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
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15 Jul 2019, 08:39
(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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