At a bakery, all donuts are priced equally and all bagels

At a bakery, all donuts are priced equally and all bagels are priced equally. What is the total price of 5 donuts and 3 bagels at the bakery?

Say the price of a donut is $x and the price of a bagel is $y. We need to find the value of 5x+3y.

(1) At the bakery, the total price of 10 donuts and 6 bagels is $12.90 --> given that 10x+6y=$12.9 --> reduce by 2: 5x+3y=$12.9/2. Sufficient.

(2) At the bakery, the price of a donut is $0.15 less than the price of a bagel --> given that x=y-0.15 --> 5x+3y=5(y-0.15)+3y. We need the value of y (or x). Not sufficient.

Answer: A.
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Video solution from Quant Reasoning:

I found the answer using both of the statements.

1) 10d + 5b = 12.90
2) d = b - 0.15
10(b-0.15)+6b=12.90
10b-1.5+6b=12.90
16b=14.4
b=0.9
[substitute for b in 2nd equation]
d=0.9-0.15=0.75
5(0.75)+3(0.9)=6.45, which is equal to 12.90(0.5)

Question asks for value of 5D + 3B.

1)10D + 6B = 12.9
5D + 3B = 12.9/2. Sufficient

2)We only have D = B - 0.15. Even after substitution of this in 5D + 3B we still have an unknown. Insufficient.

Answer is A.

This is a question based on logic you can solve in at most 20 seconds, without any calculation.

A clearly is the answer .
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We are given 5*D + 3*B = TC, so what's TC?


1) Look carefully: This simply tells us what 2TC is, so in other words it tells us what 2(5*D + 3*B) is. just take half the result and you've solved the question.

2) This tells us that 5*(B - 0.15) + 3*B = TC, but we have two unknowns and one equation, so 2 is not sufficient.

We go with A.

At a bakery, all donuts are priced equally and all bagels are priced equally. What is the total price of 5 donuts and 3 bagels at the bakery?

(1) At the bakery, the total price of 10 donuts and 6 bagels is $12.90

(2) At the bakery, the price of a donut is $0.15 less than the price of a bagel.


I understand 1) is sufficient. But I'm not understanding why 2) is insufficient. If you let price of donut be x, then price of bagel is x+0.15. Therefore 10x + 6(x + 0.15) = 12.90. Solve that and get a value for x and obviously x + 0.15.

Am I missing something obvious?

Merging similar topics. Please refer to the discussion above.

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We are given that all donuts are priced equally and all bagels are priced equally and need to determine the total price of 5 donuts and 3 bagels. Let’s start by defining some variables.

D = the price per donut

B = the price per bagel

Thus we need to determine: 5D + 3B = ?

Statement One Alone:

At the bakery, the total price of 10 donuts and 6 bagels is $12.90.

Using the information in statement one, we can create the following equation:

10D + 6B = 12.90

We can simplify the equation by dividing the entire equation by 2.

5D + 3B = 6.45

Thus, the price for 5 donuts and 3 bagels is $6.45. Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C, and E.

Statement Two Alone:

At the bakery, the price of a donut is $0.15 less than the price of a bagel.

We can express D in terms of B:

D = B - 0.15

Substituting B – 0.15 for D, we get:

5(B – 0.15) + 3B

5B – 0.75 + 3B

8B – 0.75

However, without knowing anything about the price of either D or B, or the total amount spent, we cannot determine the sum of 5D + 3B. Thus, statement two is insufficient.

The answer is A.
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While I do understand your explanation, I have a different viewpoint.

Its commonly known that if we have two unknowns , we need two equations to solve the Q.

In this Q, from(1) 10x +6y = 12.90
from (2) x = y - 0.15

If I see this, the first thing which comes to my mind is option C, ( 2 unknowns x, y and we can solve this with two equations)
How to negate this line of thought ?

Hello mqdn,

In DS each of the statement has to be checked for sufficiency in Isolation First.. Meaning, when we consider S1 the information in S2 should not be taken in consideration and Vice Versa. We need to Move to consider both statements together only if Each statement by itself is not sufficient.

In this question, Since S1 alone is sufficient, we dont even need to check for S1+S2. The correct answer is A.

PS: The AD/BCE technique by MGMAT or 12TEN method by Kaplan are both great ways to remember this.


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Hello Manonamission,

My 50 cents here.

You are absolutely right - 2 unknowns x, y and we can solve this with two equations. But if we look at the question, we dont need value of the two unknown. We need the sum of 5 donuts and 3 Bagels. This or something similar like this (Sum of unknowns) should set off an alarm for us. Maybe, Just MAYBE we dont need two equations to solve this.

Probably thats one to avoid falling into the 'C" trap in this question.

I hope this helps.



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Caution:
Price of donuts and bagels are not identical; they are different. But, within the donuts category they're priced equally (the same case for bagels too).
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given= price of each donut & bangel is same.
find price of 5 donut + 3 bangels = ?

a) 10 donut + 6 bangel = 12.9 => 2(5 donut + 3 bangel) = 12.6 =>5 donut + 3 bangel = 12.9/2
Sufficient (cancel BCE)

b)donut price < bangel price - 0.15
multiple case for unit price of bangel & donut are possible. Not sufficient (cancel D)

Answer A

Posted from my mobile device

Price of donut = d
Price of bagel = b

To find:
5d + 3b = ?

St. 1:
10d + 6b = 12.9
=> 5d + 3b = 6.45

=> St. 1 is sufficient

St. 2:
d = b - 0.15
=> 5d + 3b = 5(b - 0.15) + b = 6b - 0.75

=> St. 2 is insufficient

Answer: A
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Solution:

Let the price of each donut be a$ and that of a bagel be b$.

St (1)

10a + 6b = 12.90

=> 5a + 3b = 12.90 /2

Thus Sufficient

St (2)

Given a = b – 0.15

Thus 5a + 3b

= 5(b-0.15) + 3b

We do not know the value of a or b and hence Insufficient.

Thus option (A)


Hope this helps
Devmitra Sen (GMAT Expert-Quants)

Answer: Option A

Video solution by GMATinsight



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Hi BrentGMATPrepNow, regarding statement 2 of D=B - 0.15, substitute into 5(B - 0.15) + 3B > B = 0.094.
Using B we can find out D from 5D + 3B equation. Therefore not sure why is not sufficient and did I miss something? Thanks Brent

How did you go from 5(B - 0.15) + 3B to B = 0.094?

5(B - 0.15) + 3B is not an equation. So, how can B = 0.0094?