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15 Apr 2016, 21:55
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59% (02:22) correct
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Pam owns an inventory of unopened packages of corn and rice, which she has purchased for $17 and $13 per package, respectively. How many packages of corn does she have ?
1. She has $282 worth of packages
2. She has twice as many packages of corn as of rice
1. She has $282 worth of packages
2. She has twice as many packages of corn as of rice
08 Jun 2016, 22:28
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Vinayprajapati
Pam owns an inventory of unopened packages of corn and rice, which she has purchased for $17 and $13 per package, respectively. How many packages of corn does she have ?
1. She has $282 worth of packages
2. She has twice as many packages of corn as of rice
1. She has $282 worth of packages
2. She has twice as many packages of corn as of rice
This is an obvious C trap question. If we combine both statements, we will get an answer.
So this problem is likely to be solved by one statement only. (With experience you can say that this statement would be A)
If we take factors of 282 we get: 2*3*47.
Statement 1
17c+13r = 282 = 6 * 47. [ where c = corn packages and r = rice packages]
Note that 17 and 13 are co-prime.
Our aim is to find such values of c and r such that 17c+13r = 47.
47 = 34+13.
c=2; r=1
We can get a unique answer.
Corn Package = 2*6 = 12 (We dont need to calculate this).
Statement 2
We know that c= 2r. But we dont know exact numbers so not sufficient.
A is the answer.
Konstantin1983
I hate such questions because, as in statement 1, you must be sure that such equation doesn't have unique solution. And with such numbers..How come should i guess about 12 and 6? Picking numbers is time-consuming
This question is based on the concept of "integral solutions". Since in such real world examples, x and y cannot be negative or fractional, usually these equations have a finite number of solutions.
After you get one solution, you will quickly know how many solutions the equation has. But getting the first set of values which satisfy the equation requires a little bit of brute force.
But the good thing here is that this is a DS question. You don't need to find the actual solution. The only thing you "need" is to establish that there is a single solution only. (Obviously, there has to be a solution since she does own $282 worth of packages.)
That can be done relatively easily.
First, check out this post for a conceptual discussion on this question type (case 2):
https://anaprep.com/algebra-integer-sol ... variables/
Once you understand this, the following will make sense to you.
17x + 13y = 282
If x = 0, y is 21.something (not an integer)
If x = 1, y = 20.something
If x = 2, y = 19.something
If x = 3, y = 17.something
Now you know that there will be only one set of values satisfying this equation. Why? Because y will be less than 17 in the first set of values which satisfy this equation. So if you want to get the next set that satisfies, you will need to subtract it by 17 which will make y negative. So in any case, there will be a unique solution to this equation.
Hence statement 1 is sufficient.
Answer (A)
