A bakery sells white bread for certain price and rye bread for a certain price. If Chris, Matt and John bought bread in this bakery, how much did Chris pay for 2 white breads and 3 rye breads?
(1) Matt bought 2 white breads and 2 rye breads for $8.80.
(2) John bought 4 white breads and 6 rye breads for $22.20.
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A bakery sells white bread for certain price and rye bread
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BTGmoderatorDC
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ceilidh.erickson
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(Let's ignore the non-idiomatic pluralization "breads" rather than "loaves of bread.")...BTGmoderatorDC wrote:A bakery sells white bread for certain price and rye bread for a certain price. If Chris, Matt and John bought bread in this bakery, how much did Chris pay for 2 white breads and 3 rye breads?
(1) Matt bought 2 white breads and 2 rye breads for $8.80.
(2) John bought 4 white breads and 6 rye breads for $22.20.
Let:
w = the price of one loaf of white bread
r = the price of one loaf of rye bread
Question: 2w + 3r = ?
Keep in mind that we do not necessarily need to find the values of w and r individually; we just need the sum 2w + 3r.
(1) Matt bought 2 white breads and 2 rye breads for $8.80.
Rewrite as:
2w + 2r = 8.80
We could simplify to:
w + r = 4.40
This doesn't answer our target question, though. Insufficient.
(2) John bought 4 white breads and 6 rye breads for $22.20.
Who is buying this much bread?! Oh, well. Rewrite as:
4w + 6r = 22.20
We could simplify to:
2w + 3r = 11.10
This gives us a value for our target question! Sufficient. The answer is B.
Beware of assuming that you will always need 2 equations whenever you have 2 variables. The GMAT likes to mess with this assumption, especially in DS. See more on that here: https://www.manhattanprep.com/gmat/blog ... ons-rules/
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
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deloitte247
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Let the price of white bread = w
Let the price of rye bread = r
Question; (2 * w) + (3 * r) = ??
2w +3r
Statement 1 = Matt bought 2 white breads and 2 rye breads for $8.80
2w + 2r = $8.80
This equation has many solution because the value of w and r is not defined, hence statement 1 is NOT SUFFICIENT.
Statement 2 = John brought 4 white bread and 6 rye breads for $22.20
$$\frac{4n}{2}\ +\ \frac{6r}{2}\ =\ \frac{\left(\text{22.20}\right)}{2}$$
2w + 3r = $11.10
That is, quantity of bread bought by John is twice that of Chris, thus Chris paid $11.10 for 2 white breads and 3 rye breads.
Hence, Statement 2 is sufficient.
Option B is correct.
Let the price of rye bread = r
Question; (2 * w) + (3 * r) = ??
2w +3r
Statement 1 = Matt bought 2 white breads and 2 rye breads for $8.80
2w + 2r = $8.80
This equation has many solution because the value of w and r is not defined, hence statement 1 is NOT SUFFICIENT.
Statement 2 = John brought 4 white bread and 6 rye breads for $22.20
$$\frac{4n}{2}\ +\ \frac{6r}{2}\ =\ \frac{\left(\text{22.20}\right)}{2}$$
2w + 3r = $11.10
That is, quantity of bread bought by John is twice that of Chris, thus Chris paid $11.10 for 2 white breads and 3 rye breads.
Hence, Statement 2 is sufficient.
Option B is correct.
