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At ABC Hardware the total cost of 1 paintbrush and...

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At ABC Hardware the total cost of 1 paintbrush and...

by swerve » Mon Jan 13, 2020 4:12 pm
At ABC Hardware the total cost of 1 paintbrush and 2 rolls of tape is $6.25. What is the price of one roll of tape?

1) The price of one paintbrush is three times the price of one roll of tape.
2) The total cost of 6 rolls of tape and 3 paintbrushes is $18.75.

The OA is A

Source: Magoosh
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Source: — Data Sufficiency |
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Re: At ABC Hardware the total cost of 1 paintbrush and...

by deloitte247 » Sat Jan 25, 2020 3:30 pm
let the price of 1 paintbrush = p
let the price of 1 roll tape = r
1 (p) + 2 (r) = $6.25
2r + p = 6.25
What is the price of one roll of tape?
2r = 6.25 - p ----- eqn (1)
$$r=\frac{6.25-p}{2}\ \ \ \ ---\ eqn\ \left(2\right)$$
Statement 1: The price of one paintbrush is three times the price of one roll of tape.
p = 3r
Substituting the new value of p in eqn (1)
2r = 6.25 - p
2r + 3r = 6.25
r = 6.25/5 = $1.25
Hence, statement 1 is SUFFICIENT.

Statement 2: The total cost of 6 rolls of tape and 3 paintbrushes is $18.75
=> 6 (r) + 3 (p) = $18.75
From question sttem; 2r + p = 6.25 and p = 6.25-2r
Therefore, 6r + 3 (6.25-2r) = 18.75
6r + 18.75 - 6r = 18.75
6r - 6r = 18.75 - 18.75
This expression does not give the value of r which is the price of 1 roll of tape. Hence, statement 2 is NOT SUFFICIENT.

However, since only statement 1 is sufficient, then the correct answer choice is option A.
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