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13%
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A garden store purchased a number of shovels and a number of rakes. If the cost of each shovel was $14 and the cost of each rakes was $9, what was the total cost of the shovels and rakes purchased by the store?
(1) The ratio of the number of shovels to the number of rakes purchased by the store was 2 to 3
(2) The total number of shovels and rakes purchased by the store was 50.
(1) The ratio of the number of shovels to the number of rakes purchased by the store was 2 to 3
(2) The total number of shovels and rakes purchased by the store was 50.
EMPOWERgmatRichC
Expert
Major Poster
Joined: 19 Dec 2014
Last visit: 31 Dec 2023
Posts: 21,775
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Expert reply
Hi All,
Questions on the GMAT are always carefully worded, so you have to respect that level of detail and do the necessary work to get the answer to the question THAT IS ASKED. In DS questions, even with the same information, a difference in the wording of the question can lead to a different correct answer.
Here, we're given the price of each shovel ($14) and each rake ($9) and we're asked for the TOTAL COST of ALL the shovels and rakes purchased in the store.
To figure out TOTAL COST, we need to know the number of shovels and the number of rakes.
The math involved in solving this problem has already been explained by gmatblackbelt, so I won't rehash that here. Instead, consider how the answer changes when I just change the question.
What if the prompt asked: "Is the total cost of the shovels greater than the total cost of the rakes?" (Hint: the answer would NOT be C).
How about if it asked: "Is the combined cost of the shovels and rakes greater than $100?" (Hint: the answer is also NOT C.)
The math involved in most DS questions is not difficult, which is why DS questions aren't really there to test math skills. DS questions test you on a number of other skills that matter though, including organization, accuracy, attention-to-detail, thoroughness, the ability to PROVE that you've correct, etc. Don't let pride get in the way of picking up easy points on the GMAT - take the notes, do the necessary work and you can pick up all of these easy points.
GMAT assassins aren't born, they're made,
Rich
Questions on the GMAT are always carefully worded, so you have to respect that level of detail and do the necessary work to get the answer to the question THAT IS ASKED. In DS questions, even with the same information, a difference in the wording of the question can lead to a different correct answer.
Here, we're given the price of each shovel ($14) and each rake ($9) and we're asked for the TOTAL COST of ALL the shovels and rakes purchased in the store.
To figure out TOTAL COST, we need to know the number of shovels and the number of rakes.
The math involved in solving this problem has already been explained by gmatblackbelt, so I won't rehash that here. Instead, consider how the answer changes when I just change the question.
What if the prompt asked: "Is the total cost of the shovels greater than the total cost of the rakes?" (Hint: the answer would NOT be C).
How about if it asked: "Is the combined cost of the shovels and rakes greater than $100?" (Hint: the answer is also NOT C.)
The math involved in most DS questions is not difficult, which is why DS questions aren't really there to test math skills. DS questions test you on a number of other skills that matter though, including organization, accuracy, attention-to-detail, thoroughness, the ability to PROVE that you've correct, etc. Don't let pride get in the way of picking up easy points on the GMAT - take the notes, do the necessary work and you can pick up all of these easy points.
GMAT assassins aren't born, they're made,
Rich
Posts: 1,138
blog
1: ratio of 2/3 no help here we could have an infinite amount of rakes and shovels so long as the ratio is 2/3
2: We don't know how many rakes were bought or how many shovels, the price would be different.
5x=50 x=10 so 2(14)+3(9) --> 28+27 = 55$*10 --> 550$.
C
General Discussion
GMATBLACKBELT
i made the very silly mistake of thinking that the ratio by itself was enough. note to self: you need absolute numbers for things like this because the numbers can be very different but still maintain the same ratio.
isn't A sufficient for this question/
9X + 14Y / X + Y we have to find this out given X / Y = 2/3
9X + 14Y / X + Y we have to find this out given X / Y = 2/3
fozzzy
Consider this:
If shovels=2 and rakes=3, then the total cost is 2*14+3*9.
If shovels=4 and rakes=6, then the total cost is 4*14+6*9.
So, the first statement is not sufficient.
Hope it's clear.
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EMPOWERgmatRichC
Great Insight Rich...
Posts: 2
I have question. What is GMAT trying to testing through such a simple question? My problem is, when I take my mocks, I waste time thinking if there's something I'm missing because the answer can't be this easy. Anyone else who feels the same? Or, any am I approaching this all wrong?
ssmissiongmat
You have partly answered the question. The GMAT is testing whether you are operating with a clear mind to arrive at the correct answer. If you find yourself spending too much time, then the GMAT will penalize you later when you will be unable to correctly answer other questions. The GMAT quantitative section is also a test of reasoning and testing abilities.
Posts: 4
blog
550 would be the cost of total content
Posted from my mobile device
GMAT 1: 760 Q51 V42
Posts: 10,057
Forget the conventional way to solve DS questions.
We will solve this DS question using the variable approach.
DS question with 2 variables : Let the original condition in a DS question contain 2 variables . In other words, there are two fewer equations than variables. Now, we know that each condition (1) and (2) would usually give us an equation, however, since we need 2 equations to match the numbers of variables and equations in the original condition, the unequal number of equations and variables should logically give us an answer C.
To master the Variable Approach, visit https://www.mathrevolution.com and check our lessons and proven techniques to score high in DS questions.
Let’s apply the 3 steps suggested previously. [Watch lessons on our website to master these 3 steps]
Step 1 of the Variable Approach: Modifying and rechecking the original condition and the question.
=> Let us assign variable: Shovels(s) and Rakes (r).
- Cost - Each Shovel($14) and Each Rake($9)
We have to find value of 14s + 9r.
Second and the third step of Variable Approach: From the original condition, we have 2 variables (s and r).To match the number of variables with the number of equations, we need 2 equations. Since conditions (1) and (2) will provide 1 equation each, C would most likely be the answer.
Let’s take a look at both conditions together .
Condition(1) tells us that s : r = 2 : 3 .
=> For a number 'x', ratio of s: r = 2x : 3x ----------(1)
Condition(2) tells us that s + r = 50.
=> 2x + 3x = 50
=> 5x = 50 => x = 10 and hence s = 20 and r = 30.
=> Substituting the value of 's' and 'r' in 14s + 9r we will get the total cost.
Since the answer will be unique, both conditions together are sufficient by CMT 2.
So, C is the correct answer.
Answer: C
We will solve this DS question using the variable approach.
DS question with 2 variables : Let the original condition in a DS question contain 2 variables . In other words, there are two fewer equations than variables. Now, we know that each condition (1) and (2) would usually give us an equation, however, since we need 2 equations to match the numbers of variables and equations in the original condition, the unequal number of equations and variables should logically give us an answer C.
To master the Variable Approach, visit https://www.mathrevolution.com and check our lessons and proven techniques to score high in DS questions.
Let’s apply the 3 steps suggested previously. [Watch lessons on our website to master these 3 steps]
Step 1 of the Variable Approach: Modifying and rechecking the original condition and the question.
=> Let us assign variable: Shovels(s) and Rakes (r).
- Cost - Each Shovel($14) and Each Rake($9)
We have to find value of 14s + 9r.
Second and the third step of Variable Approach: From the original condition, we have 2 variables (s and r).To match the number of variables with the number of equations, we need 2 equations. Since conditions (1) and (2) will provide 1 equation each, C would most likely be the answer.
Let’s take a look at both conditions together .
Condition(1) tells us that s : r = 2 : 3 .
=> For a number 'x', ratio of s: r = 2x : 3x ----------(1)
Condition(2) tells us that s + r = 50.
=> 2x + 3x = 50
=> 5x = 50 => x = 10 and hence s = 20 and r = 30.
=> Substituting the value of 's' and 'r' in 14s + 9r we will get the total cost.
Since the answer will be unique, both conditions together are sufficient by CMT 2.
So, C is the correct answer.
Answer: C
Posts: 4,849
A garden store purchased a number of shovels and a number of rakes. If the cost of each shovel was $14 and the cost of each rakes was $9, what was the total cost of the shovels and rakes purchased by the store?
Let the number of shovels purchased be S and the number of rakes purchased be R , then we need to find the total cost of shovels and rakes purchased. Cost of each shovel and rakes is given in the question. So we need to S and R is the answer the question stem.
(1) The ratio of the number of shovels to the number of rakes purchased by the store was 2 to 3
S/R = 2/3
We cannot find the actual value of S and R from the ratio given.
St 1 alone is insufficient.
(2) The total number of shovels and rakes purchased by the store was 50.
S + R = 50
We cannot find the exact value of S and R from this equation.
St 2 is also insufficient.
Combining 1 and 2 , you can find the definite value of S and R.
S+ R = 50 and S/R = 2/3 => S = (2/3)*R
On solving, you will get the definite value for S and R and the total cost of purchase can also be calculated.
Option C is the answer.
Thanks,
Clifin J Francis,
GMAT SME
Let the number of shovels purchased be S and the number of rakes purchased be R , then we need to find the total cost of shovels and rakes purchased. Cost of each shovel and rakes is given in the question. So we need to S and R is the answer the question stem.
(1) The ratio of the number of shovels to the number of rakes purchased by the store was 2 to 3
S/R = 2/3
We cannot find the actual value of S and R from the ratio given.
St 1 alone is insufficient.
(2) The total number of shovels and rakes purchased by the store was 50.
S + R = 50
We cannot find the exact value of S and R from this equation.
St 2 is also insufficient.
Combining 1 and 2 , you can find the definite value of S and R.
S+ R = 50 and S/R = 2/3 => S = (2/3)*R
On solving, you will get the definite value for S and R and the total cost of purchase can also be calculated.
Option C is the answer.
Thanks,
Clifin J Francis,
GMAT SME
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almost fell for the trap , that this was a difficult qn hehe
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