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Sub 505 (Easy)|   Math Related|         
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12 Days of Christmas GMAT Competition - Day 2: An artisan bakery sells 17 Dec 2024, 09:00
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Whole wheat loaves: 350 Rye loaves: 250
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Question Stats:

94% (01:30) correct 6% (01:18) wrong based on 473 sessions

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12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes

 


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An artisan bakery sells three types of bread: whole wheat, sourdough, and rye. In a certain month, sourdough sales account for 40% of the total loaves sold and exceed rye sales by 150 loaves.

If the bakery sold 1,000 loaves in that month, select for Whole wheat loaves the number of whole wheat loaves sold, and select for Rye loaves the number of rye loaves sold in that month. Make only two selections, one in each column.
Whole wheat loaves Rye loaves
150
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250
350
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Whole wheat loaves: 350 Rye loaves: 250
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12 Days of Christmas GMAT Competition - Day 2: An artisan bakery sells 17 Dec 2024, 10:00
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An artisan bakery sells three types of bread: whole wheat, sourdough, and rye. In a certain month, sourdough sales account for 40% of the total loaves sold and exceed rye sales by 150 loaves.

If the bakery sold 1,000 loaves in that month, select for Whole wheat loaves the number of whole wheat loaves sold, and select for Rye loaves the number of rye loaves sold in that month. Make only two selections, one in each column.
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GMAT Club's Official Explanation:



The bakery sold 1,000 loaves in a month, divided among whole wheat, sourdough, and rye.

Sourdough accounted for 40% of total sales:
Sourdough loaves = 0.4 * 1000 = 400

Sourdough loaves exceeded rye loaves by 150:
Rye loaves = 400 - 150 = 250

Whole wheat loaves:
Whole Wheat loaves = 1000 - 400 - 250 = 350
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12 Days of Christmas GMAT Competition - Day 2: An artisan bakery sells 17 Dec 2024, 09:25
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as in the question there are three types of bread whole wheat , sourdough, and rye
since sourdough sales accounts for 40% in certain month and exceeds rye sales by 150loaves
in that month bakery sold 1000 loaves so to find out whole wheat and rye
since bakery sold 1000 loaves and sourdough is 40%
so sourdough = 1000 x 40% = 400 loaves sold that month
as sourdough exceeds rye sales by 150 loaves
therefore rye =400 - 150 = 250 so we got rye
let the wholewheat be x
so x + 400 +250 = 1000
x + 650 = 1000
x = 1000 - 650
x = 350
so rye = 250 and whole wheat = 350
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12 Days of Christmas GMAT Competition - Day 2: An artisan bakery sells 17 Dec 2024, 09:45
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Total loaves sold=1,000

Sourdough sales= 40/100*1000= 400 units of sourdough
1,000-400=600(remaining units of both Whole Wheat and Rye bread sold)

Rye sales= 400-150
=250

Whole Wheat sales= 600-250
=350
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Three types of Bread: whole wheat, sourdough, and rye. Let's call the number of each bread type as x,y,z respectively. We already know that y is 40%. So x+z is 60%.

By using the total bread count 1000, we can say y = 400 and x+z=600.

y is 150 more than z. So, z is 250 = 400 - 150. From this we can find x = 350 (Since x+z=600).

Whole wheat loaves are 350 and Rye loaves are 250.
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12 Days of Christmas GMAT Competition - Day 2: An artisan bakery sells 17 Dec 2024, 09:46
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let wholeweat, sd and rye are denoted by x,y,z
given y is 40% of (x+y+z)
and x+y+z= 1000

therefore y=.4*1000=400
y=z+150 --> z=250

x= 1000- 250- 400= 350
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12 Days of Christmas GMAT Competition - Day 2: An artisan bakery sells 17 Dec 2024, 09:50
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An artisan bakery sells three types of bread: whole wheat, sourdough, and rye. In a certain month, sourdough sales account for 40% of the total loaves sold and exceed rye sales by 150 loaves.

If the bakery sold 1,000 loaves in that month, select for Whole wheat loaves the number of whole wheat loaves sold, and select for Rye loaves the number of rye loaves sold in that month. Make only two selections, one in each column.
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We are tasked with determining the number of whole wheat and rye loaves sold in a month where the bakery sold 1,000 loaves in total. Let’s solve step by step.
[hr]
Given:
  1. Total loaves sold: 1,000.
  2. Sourdough accounts for 40% of total loaves sold: Sourdough loaves=0.4×1,000=400.\text{Sourdough loaves} = 0.4 \times 1,000 = 400.
  3. Sourdough sales exceed rye sales by 150 loaves: Rye loaves+150=400 ⟹ Rye loaves=250.\text{Rye loaves} + 150 = 400 \implies \text{Rye loaves} = 250.
  4. Remaining loaves are whole wheat: Whole wheat loaves=Total loaves−(Sourdough loaves+Rye loaves).\text{Whole wheat loaves} = \text{Total loaves} - (\text{Sourdough loaves} + \text{Rye loaves}). Substituting values: Whole wheat loaves=1,000−(400+250)=350.\text{Whole wheat loaves} = 1,000 - (400 + 250) = 350.
[hr]
Selections:
  • Whole wheat loaves: 350.
  • Rye loaves: 250.
[hr]
Final Answer:
  • Whole wheat loaves: 350.
  • Rye loaves: 250.
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12 Days of Christmas GMAT Competition - Day 2: An artisan bakery sells 17 Dec 2024, 09:52
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An artisan bakery sells three types of bread: whole wheat, sourdough, and rye. In a certain month, sourdough sales account for 40% of the total loaves sold and exceed rye sales by 150 loaves.

If the bakery sold 1,000 loaves in that month, select for Whole wheat loaves the number of whole wheat loaves sold, and select for Rye loaves the number of rye loaves sold in that month. Make only two selections, one in each column.

Sourdough = Rye + 150
Sourdough = 40% (Sourdough + Rye + Whole wheat) = 40%*1000 = 400
Rye = 400 - 150 = 250
Whole wheat = 1000 - 400 - 250 = 350

Whole wheat loavesRye loaves
350250
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12 Days of Christmas GMAT Competition - Day 2: An artisan bakery sells 17 Dec 2024, 09:53
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Sourdough = 40/100 total sales = 40/100*1000 = 400 loaves
Rye = Sourdough - 150= 400-150 = 250 loaves
Whole wheat = 1000-400-250= 350 loaves
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Let the number of whole wheat, sourdough, and rye be w, s and r respectively then,

40% of total sales = sourdough sales
(w + s + r)(2/5) = s
2w + 2s + 2r = 5s --- (1)

sourdough sales is 150 more than rye sales
s - 150 = r --- (2)

Total sales = 1000
w + s + r = 1000 --- (3)

From (1) and (3)

5s = 2*1000
s = 400

Substituting s in (2) => r = 250
Substituting s and r in (3) => 400 + 250 + w = 1000 => w = 350

Hence, the answer is 350 and 250.
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12 Days of Christmas GMAT Competition - Day 2: An artisan bakery sells 17 Dec 2024, 09:55
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We are given that the total number of loaves is 1000.
40 % of 1000 = 400 consists of Sugerdough,
150 + Rye = Sugerdough (given), so Rye = 250
Finally WholeWheat + Rye + Sugerdough = 1000
So W + 250 + 400 = 1000.
W = 350

So WholeWheat loaves = 350 and Rye loaves = 250
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If we just form the equation for the number of loaves it is:
w + 2x + 150 = 1000
w+2x = 850 (x = rye loaves)
> Plugged values for x from table to see which values of w are feasible for e.g. 150 is ruled out, we dont have any value w > 500 in the table. After ellimination, only left with w = 350, and x = 250
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12 Days of Christmas GMAT Competition - Day 2: An artisan bakery sells 17 Dec 2024, 10:07
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s= 40% of 1000= 400
s= r+150= r= 400-150= 250
w= 1000-400-250= 350
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Total loaves: 1000

S = 40% of total loaves = 400

S - R = 150 ==> R = 400 - 150 = 250

W must be 350 ==> 1000 - (250 + 400) = 350

First column: value of Whole Wheat (W) = 350

Second column: value of Rye (R) = 250
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S / S+W+R = 2/5

S = R+150

S+W+R = 1000

=> S = 400
=> R = 250
=> W = 1000 - 650 = 350

Answer 350, 250
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To find the number of each type of bread sold:

1. We know the bakery sold a total of 1,000 loaves.
2. Sourdough sales account for 40% of the total, which means there are 400 sourdough loaves.
3. Sourdough exceeds rye sales by 150 loaves, so if there are 400 sourdough loaves, there are 250 rye loaves (400 - 150).
4. Subtracting the rye loaves from the total gives us 350 whole wheat loaves.

Number of whole wheat loaves: 350
Number of rye loaves: 250
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12 Days of Christmas GMAT Competition - Day 2: An artisan bakery sells 17 Dec 2024, 10:24
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total loaves = 1000

sourdough is 40% which is 400 loaves
also soardough is 150 more than rye, 400 - 150 = 250
total rye loaves is 250
remaining are the whole wheat loaves
1000 - 400 - 250 = 350

hence Whole wheat = 350loaves, rye = 250 loaves
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An artisan bakery sells three types of bread: whole wheat, sourdough, and rye. In a certain month, sourdough sales account for 40% of the total loaves sold and exceed rye sales by 150 loaves.

If the bakery sold 1,000 loaves in that month, select for Whole wheat loaves the number of whole wheat loaves sold, and select for Rye loaves the number of rye loaves sold in that month. Make only two selections, one in each column.
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12 Days of Christmas GMAT Competition - Day 2: An artisan bakery sells 17 Dec 2024, 10:25
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W, S , R
S=0.4(S+W+R),---(1)
S-R=150 ---(2)
S+W+R=1000; ---(3)

S=0.4*1000=S=400
R=400-150=250
W=1000-250-400=350

(350,250)
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Given Information:
Total loaves sold in the month = 1,000 loaves.
Sourdough sales account for 40% of the total loaves sold.
Sourdough sales exceed rye sales by 150 loaves.
Calculations:
Step 1: Calculate Sourdough Sales
Sourdough sales = 40% of 1,000 loaves.
Sourdough sales
=
0.40
×
1000
=
400
loaves
Sourdough sales=0.40×1000=400 loaves
Step 2: Calculate Rye Sales
Let
R
R be the number of rye loaves sold.
According to the problem, sourdough sales exceed rye sales by 150 loaves.
400
=
R
+
150
400=R+150
R
=
400
−
150
R=400−150
R
=
250
loaves
R=250 loaves
Step 3: Calculate Whole Wheat Sales
Let
W
W be the number of whole wheat loaves sold.
Total loaves sold = Whole wheat loaves + Sourdough loaves + Rye loaves.
1000
=
W
+
400
+
250
1000=W+400+250
1000
=
W
+
650
1000=W+650
W
=
1000
−
650
W=1000−650
W
=
350
loaves
W=350 loaves
Selections:
Whole wheat loaves: 350
Rye loaves: 250
So, the correct selections are:

Whole wheat loaves: 350
Rye loaves: 250
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given 40% are Sourdough, i.e 40% of 1000 = 400 sourdough

Rye = 400-150=250

and hence remaining is wheat = 1000-(400+250) = 350
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