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# In a bakery, 70% of the doughnuts are glazed. If glazed doughnuts acco

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Math Expert
Joined: 02 Sep 2009
Posts: 51071
In a bakery, 70% of the doughnuts are glazed. If glazed doughnuts acco  [#permalink]

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09 Feb 2017, 00:27
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Difficulty:

15% (low)

Question Stats:

83% (01:46) correct 17% (01:43) wrong based on 123 sessions

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In a bakery, 70% of the doughnuts are glazed. If glazed doughnuts account for 21% of all pastries in the bakery, what percent of all pastries in the bakery are doughnuts?

A. 14.7%
B. 24%
C. 28%
D. 30%
E. 35%

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Re: In a bakery, 70% of the doughnuts are glazed. If glazed doughnuts acco  [#permalink]

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09 Feb 2017, 00:46
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1
Bunuel wrote:
In a bakery, 70% of the doughnuts are glazed. If glazed doughnuts account for 21% of all pastries in the bakery, what percent of all pastries in the bakery are doughnuts?

A. 14.7%
B. 24%
C. 28%
D. 30%
E. 35%

Led D be total Doughnuts, G be Glazed Doughnuts, and P be the total pastries.
70% of the doughnuts are glazed => 0.7D = G
glazed doughnuts account for 21% of all pastries => G = 0.21P

0.7D = 0.21P => D/P = 0.3 => 30%

Hence Option D is correct.
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In a bakery, 70% of the doughnuts are glazed. If glazed doughnuts acco  [#permalink]

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09 Feb 2017, 01:25
1
Bunuel wrote:
In a bakery, 70% of the doughnuts are glazed. If glazed doughnuts account for 21% of all pastries in the bakery, what percent of all pastries in the bakery are doughnuts?

A. 14.7%
B. 24%
C. 28%
D. 30%
E. 35%

70% glazed doughnuts = 21% pastries

100% doughnuts = X% pasties

X% pastries = $$\frac{(100*21)}{70}$$ pastries = 30% pasties

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Re: In a bakery, 70% of the doughnuts are glazed. If glazed doughnuts acco  [#permalink]

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11 Mar 2017, 13:53
try smart numbers: e.g. total 100 donats, then 70 glazed
70-21
?-100
total number of pastries is 7000/21
100/ (7000/21)=2100/7000=21/70=3/10=30%
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Re: In a bakery, 70% of the doughnuts are glazed. If glazed doughnuts acco  [#permalink]

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11 Mar 2017, 14:17
is this a 600-700 question or lesser?
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Joined: 02 Sep 2009
Posts: 51071
Re: In a bakery, 70% of the doughnuts are glazed. If glazed doughnuts acco  [#permalink]

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12 Mar 2017, 02:55
praneet87 wrote:
is this a 600-700 question or lesser?

Check the difficulty level of a question in tags and in original post's stats.
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Re: In a bakery, 70% of the doughnuts are glazed. If glazed doughnuts acco  [#permalink]

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06 Jun 2017, 20:36
Bunuel wrote:
In a bakery, 70% of the doughnuts are glazed. If glazed doughnuts account for 21% of all pastries in the bakery, what percent of all pastries in the bakery are doughnuts?

A. 14.7%
B. 24%
C. 28%
D. 30%
E. 35%

Using algebra we can disentangle this problem and translate it into a relatively simple fraction- without actually having to pick numbers or test values- they key to understanding this question is knowing that if 70% of doughnuts comprises 21% of ALL pastries, then 70 percent of the doughnuts divided by .21 will give you the total number of pastries. And of course if we know that 70% of all doughnuts are glazed then we must also know the total number of doughnuts.

Total Doughnuts/ All Pastries = answers
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Re: In a bakery, 70% of the doughnuts are glazed. If glazed doughnuts acco  [#permalink]

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10 Jun 2017, 06:35
Bunuel wrote:
In a bakery, 70% of the doughnuts are glazed. If glazed doughnuts account for 21% of all pastries in the bakery, what percent of all pastries in the bakery are doughnuts?

A. 14.7%
B. 24%
C. 28%
D. 30%
E. 35%

We can let the total number of pastries = p, the number of donuts = d, and the number of glazed donuts = g. We want to determine d/p x 100%, which is the expression for the percentage of donuts in the bakery.

Let’s create the following equation:

0.7d = g

g = 0.21p

Since both equations equal g, we can equate them. Thus, we have:

0.7d = 0.21p

d = 0.21p/0.7

d = 0.3p

We need to determine (d/p) x 100%:

(0.3p/p) x 100% = 0.3 x 100% = 30%

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In a bakery, 70% of the doughnuts are glazed. If glazed doughnuts acco  [#permalink]

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05 Aug 2018, 07:50
Bunuel wrote:
In a bakery, 70% of the doughnuts are glazed. If glazed doughnuts account for 21% of all pastries in the bakery, what percent of all pastries in the bakery are doughnuts?

A. 14.7%
B. 24%
C. 28%
D. 30%
E. 35%

Use smart numbers. The 21% figure is not straightforward. Try 60 or 120. Both integers often work with unusual percentages.

# of doughnuts = $$60$$

# of glazed doughnuts = $$42$$
70 percent of 60 doughnuts are glazed
$$0.7*60=42$$ glazed doughnuts

Total # of pastries
42 glazed doughnuts equal 21% of all Pastries, P
$$42=.21P$$
$$P=\frac{42}{.21}=\frac{4,200}{21}=200$$ Pastries

Doughnuts are what percent of all pastries?
D = 60, P = 200

Percent: $$(\frac{Part}{Whole}*100)=(\frac{D}{P}*100)$$
Percent: $$(\frac{60}{200}*100)=(\frac{3}{10}*100)=(.30*100)=$$

$$30$$ percent

In a bakery, 70% of the doughnuts are glazed. If glazed doughnuts acco &nbs [#permalink] 05 Aug 2018, 07:50
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