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Spaceland Prep Strategy Question #5

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Spaceland Prep Strategy Question #5

by spaceland prep » Tue Mar 15, 2011 6:46 am
Q. A shrewd opportunist bought 50 Kale Kids in November for t dollars total. In December, he sold each Kale Kid for a profit of 150 percent. In terms of t, how much was each Kale Kid sold for?

(A) t/20

(B) 5t/2

(C) 250t

(D) t/100 + 150

(E) 250/t

Think about the units this question uses: dollars and Kids. The answer, t, represents a dollar amount. Which answers don't have units of dollars? If t is the cost for 50 Kale Kids, which remaining answers will be too large to represent the value that one Kale Kid is sold for?

Solution

[spoiler]Only the first three answers have units equivalent to dollars. (D) adds 150, which does not represent a dollar amount. (E) has units of one over dollars.

Both (B) and (C) will be larger than t. As shrewd as our friend is, he isn't going to pull in that kind of profit per Kid. (A) must be correct.

Word problems with variables in their answer choices may be vulnerable to a unit analysis. Look for this when the questions asks for something quantifiable and the variables in the answers are exposed to different operations in different choices.[/spoiler]
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by force5 » Tue Mar 15, 2011 7:10 am
one kale kids cost price is t/50
sold @150% profit or 3/2 or cost

ie- t/50 ( 1+3/2) = t/20 (hence answer A)
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by shashank.ism » Tue Mar 15, 2011 8:59 am
hey spaceland prep if there is such a simple mathematical solution for this question .. why would we analyse that way..
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by spaceland prep » Tue Mar 15, 2011 10:06 am
shashank.ism wrote:hey spaceland prep if there is such a simple mathematical solution for this question .. why would we analyse that way..
Simple mathematical solutions for some are hopeless enigmas for others. But the real benefit to this idea is that it applies to any question asking for a unit-defined quantity, regardless of difficulty.
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by shashank.ism » Tue Mar 15, 2011 6:39 pm
But you cant be very sure with these type of solutions and ultimately land up with wrong solution.
For eg. IF we go by question, cost of 50 kale is t dollars which shows that "t" is dimensionless and its unit is dollar.

though in answers no unit is specified.... If we go by your method, its very clear that option D & E could be a solution too...


Also here u discard B & C by saying both B & C will be larger than A. Since here there are 50 kale, its OK . What if a question is being set a bit easier and instead of 50 there would have been only 2 kale. Also these types of solution is highly recommended for PHYSICS problems in Unit and Dimension and not for any mathematical problems

I don't think such solutions are at all required and I urge people here not to follow these type of solutions atleast for questions which can be solved easily. And if any students feels mathematical solutions a bit tougher, please try to practice it...instead of running behind shortcuts..


P.S. Shortcuts only work for you, when you have command over subject, your basics is clear and you can solve the problem with long method. If you are not able to solve problems by proper method, shortcuts will certainly lead you to crapy answers.
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by Night reader » Tue Mar 15, 2011 7:32 pm
"nice" problem :oops:
we need to learn from its content and the suggested solution method too ...

A shrewd opportunist bought 50 Kale Kids in November for t dollars total.

Let's define the number of Kale Kids = N, the cost of each Kale Kid = C, then N=50 and total cost for N=50 Kale Kids will make N*C=t ONLY IF each Kale Kid has the same cost otherwise C belongs to the set of 50 different cost values summed to the amount of t.

In December, he sold each Kale Kid for a profit of 150 percent. In terms of t, how much was each Kale Kid sold for?

each Kale Kid for a profit of 150 percent ---> C*150% OR t/50 *1.5 Is solvable ONLY IF we know C (cost of each Kale Kid) OR given the condition for C. Otherwise we should not touch this problem, as the one is missing per Kale Kid cost data

IOM Please explain the content of this problem
spaceland prep wrote:Q. A shrewd opportunist bought 50 Kale Kids in November for t dollars total. In December, he sold each Kale Kid for a profit of 150 percent. In terms of t, how much was each Kale Kid sold for?

(A) t/20

(B) 5t/2

(C) 250t

(D) t/100 + 150

(E) 250/t

Think about the units this question uses: dollars and Kids. The answer, t, represents a dollar amount. Which answers don't have units of dollars? If t is the cost for 50 Kale Kids, which remaining answers will be too large to represent the value that one Kale Kid is sold for?

Solution

[spoiler]Only the first three answers have units equivalent to dollars. (D) adds 150, which does not represent a dollar amount. (E) has units of one over dollars.

Both (B) and (C) will be larger than t. As shrewd as our friend is, he isn't going to pull in that kind of profit per Kid. (A) must be correct.

Word problems with variables in their answer choices may be vulnerable to a unit analysis. Look for this when the questions asks for something quantifiable and the variables in the answers are exposed to different operations in different choices.[/spoiler]
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by spaceland prep » Wed Mar 16, 2011 6:36 am
shashank.ism wrote:But you cant be very sure with these type of solutions and ultimately land up with wrong solution.
For eg. IF we go by question, cost of 50 kale is t dollars which shows that "t" is dimensionless and its unit is dollar.
That's a great point, but the GMAT always acts like variables have units.
shashank.ism wrote:
P.S. Shortcuts only work for you, when you have command over subject, your basics is clear and you can solve the problem with long method. If you are not able to solve problems by proper method, shortcuts will certainly lead you to crapy answers.
These strategies are not intended to replace mathematical knowledge. They are intended to help people think about the GMAT in alternate ways. However, if one can't solve a problem mathematically, then one needs to have alternate approaches.
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by spaceland prep » Wed Mar 16, 2011 6:45 am
Night reader wrote:"nice" problem :oops:
we need to learn from its content and the suggested solution method too ...

A shrewd opportunist bought 50 Kale Kids in November for t dollars total.

Let's define the number of Kale Kids = N, the cost of each Kale Kid = C, then N=50 and total cost for N=50 Kale Kids will make N*C=t ONLY IF each Kale Kid has the same cost otherwise C belongs to the set of 50 different cost values summed to the amount of t.

In December, he sold each Kale Kid for a profit of 150 percent. In terms of t, how much was each Kale Kid sold for?

each Kale Kid for a profit of 150 percent ---> C*150% OR t/50 *1.5 Is solvable ONLY IF we know C (cost of each Kale Kid) OR given the condition for C. Otherwise we should not touch this problem, as the one is missing per Kale Kid cost data

IOM Please explain the content of this problem
While the content of the problem is secondary to the strategy being shown, these kinds of ambiguities exist on the GMAT (see Official Guide problem solving question 84).
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by GMATGuruNY » Wed Mar 16, 2011 9:07 am
spaceland prep wrote:Q. A shrewd opportunist bought 50 Kale Kids in November for t dollars total. In December, he sold each Kale Kid for a profit of 150 percent. In terms of t, how much was each Kale Kid sold for?

(A) t/20

(B) 5t/2

(C) 250t

(D) t/100 + 150

(E) 250/t
We can plug in a value for t.
Let t = 100.
Cost of each Kale Kid = 100/50 = 2.
150% profit = 1.5*2 = 3.
Selling price = cost + profit = 2+3 = 5. This is our target.

Now we plug t=100 into all the answers to see which yields our target of 5.

Only answer choice A works:
t/20 = 100/20 = 5.

The correct answer is A.
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by shashank.ism » Wed Mar 16, 2011 1:24 pm
spaceland prep wrote:
shashank.ism wrote:
P.S. Shortcuts only work for you, when you have command over subject, your basics is clear and you can solve the problem with long method. If you are not able to solve problems by proper method, shortcuts will certainly lead you to crapy answers.
These strategies are not intended to replace mathematical knowledge. They are intended to help people think about the GMAT in alternate ways. However, if one can't solve a problem mathematically, then one needs to have alternate approaches.
I really appreciate your concern & surely people should think of alternate ways to solve problems wherever required. It may help in solving problem faster. Regarding this problem I would say, it is not a right example for showing advantages of alternate ways... :).. you can give other examples..
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by spaceland prep » Thu Mar 17, 2011 9:15 am
Try to apply this concept to PS #116 in the Quantitative Review (both editions). Only one answer choice has the correct units.
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