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Manager  Joined: 02 Dec 2012
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At a bakery, all donuts are priced equally and all bagels  [#permalink]

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Question Stats: 75% (00:57) correct 25% (01:12) wrong based on 1397 sessions

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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.
Math Expert V
Joined: 02 Sep 2009
Posts: 58297
Re: At a bakery, all donuts are priced equally and all bagels  [#permalink]

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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.

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Re: At a bakery, all donuts are priced equally and all bagels  [#permalink]

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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)
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Re: At a bakery, all donuts are priced equally and all bagels  [#permalink]

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1
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.

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Re: At a bakery, all donuts are priced equally and all bagels  [#permalink]

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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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Manager  Joined: 12 Jan 2013
Posts: 142
Re: At a bakery, all donuts are priced equally and all bagels  [#permalink]

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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.

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.
Intern  Joined: 10 Jul 2014
Posts: 3
Donut and bagel at bakery question  [#permalink]

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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?
Math Expert V
Joined: 02 Sep 2009
Posts: 58297
Re: At a bakery, all donuts are priced equally and all bagels  [#permalink]

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JaredL wrote:
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?

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Re: At a bakery, all donuts are priced equally and all bagels  [#permalink]

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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.

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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Manager  Joined: 11 Jul 2016
Posts: 78
Re: At a bakery, all donuts are priced equally and all bagels  [#permalink]

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ScottTargetTestPrep wrote:
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.

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.

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 ?
Manager  G
Joined: 12 Jun 2016
Posts: 212
Location: India
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Re: At a bakery, all donuts are priced equally and all bagels  [#permalink]

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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.

mqdn wrote:
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)

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Manager  G
Joined: 12 Jun 2016
Posts: 212
Location: India
WE: Sales (Telecommunications)
Re: At a bakery, all donuts are priced equally and all bagels  [#permalink]

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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.

Manonamission wrote:
ScottTargetTestPrep wrote:
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.

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.

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 ?

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Re: At a bakery, all donuts are priced equally and all bagels  [#permalink]

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_________________ Re: At a bakery, all donuts are priced equally and all bagels   [#permalink] 05 Aug 2019, 12:59
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