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og 12 question number 87

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og 12 question number 87

by hutch27 » Thu May 09, 2013 8:43 am
Is the number of seconds required to travel d1 feet at r1 feet per second greater than the number of seconds required to travel d2 feet at r2 feet per second?
(1) d1 is 30 greater than d2.
(2) r1 is 30 greater than r2.

OA is E

I got this right but by plugging in numbers. I watched a video of this problem and saw the more algebraic approach but i'm a little confused about it, particularly how to be confident on what i'm doing is right. I'm also wondering if the writers of this question are star wars fans lol

d1=30+d2
r1=30+r2

30+d2/30+r2 > d2/r2 <--- thats what u get by combining both statements using algebra. had i done it that way i would have probably picked C

30d2+r2d2> 30r2+r2d2
cancel out r2d2
divide by 30
d2>r2 insufficient

how would one reconidze that 30+d2/30+r2 is not greater than d2/r2 Thats where i got confused
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by Atekihcan » Thu May 09, 2013 9:23 am
hutch27 wrote:d1=30+d2
r1=30+r2

30+d2/30+r2 > d2/r2 <--- thats what u get by combining both statements using algebra. had i done it that way i would have probably picked C
That's not true.
Only thing you can get by combining these two information is d1/r1 = (30 + d2)/(30 + r2)

These kind of things are difficult to disprove using algebra. Using algebra you just know that the given information in no way means that (30+d2)/(30+r2) > d2/r2. And then try to pick some numbers and prove what you know.

This is like a < b and x < y, is a/x < b/y (a, b, x, and y are all positive)?
Basic rule of inequality : we cannot divide two inequalities like that and conclude a/x < b/y.
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by GMATGuruNY » Thu May 09, 2013 11:06 am
the question goes like this
Is the number seconds required to travel d1 feet at r1 feet per second greater than the number of seconds required to travel d2 feet at r2 feet per second?

(1) d1 is 30 greater than d2
(2) r1 is 30 greater than r2
Is d1/r1 > d2/r2?

Clearly, neither statement alone is sufficient.

Statements combined:
Since d1=d2+30 and r1=r2+30, the question stem can be rephrased as follows:
Is (d2 + 30)/(r2 + 30) > d2/r2?

In words:
Does adding the same positive value (in this case, 30) to both the numerator and the denominator of a positive fraction (in this case, d2/r2) yield a fraction greater than the original fraction?

Case 1: If the numerator < the denominator, then adding the same positive value to both the numerator and the denominator results in a fraction GREATER than the original fraction.
If d2 = 1 and r2 = 2, then:
d2/r2 = 1/2.
(d2 + 30)/(r2 + 30) = 31/32.
Here, the resulting fraction (31/32) is GREATER than the original fraction.

Case 2: If the numerator = the denominator, then adding the same positive value to both the numerator and the denominator results in a fraction EQUAL to the original fraction.
If d2 = 2 and r2 = 2, then:
d2/r2 = 2/2 =1.
(d2 + 30)/(r2 + 30) = 32/32 = 1.
Here, the resulting fraction (32/32) is EQUAL to the original fraction (2/2).

Case 3: If the numerator > the denominator, then adding the same positive value to both the numerator and the denominator results in a fraction SMALLER than the original fraction.
If d2 = 2 and r2 = 1, then:
d2/r2 = 2/1 = 2.
(d2 + 30)/(r2 + 30) = 32/31.
Here, the resulting fraction (32/31) is SMALLER than the original fraction (2/1).

Thus, when the two statements are combined, it is not possible to determine whether (d2 + 30)/(r2 + 30) > d2/r2.

The correct answer is E.
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