Which of the following fractions has the greatest value? (A

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alanforde800Maximus: Master | Next Rank: 500 Posts; Posts: 187; Joined: Tue Sep 13, 2016 12:46 am

by alanforde800Maximus » Thu May 10, 2018 6:37 am

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Which of the following fractions has the greatest value?

(A) 1/(3^2)(5^2)
(B) 2/(3^2)(5^2)
(C) 7/(3^3)(5^2)
(D) 45/(3^3)(5^3)
(E) 75/(3^4)(5^5)

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Source: Beat The GMAT — Problem Solving | Thu May 10, 2018 6:37 am

Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members; Thanked: 6 times

by Vincen » Wed May 23, 2018 1:06 am

alanforde800Maximus wrote:Which of the following fractions has the greatest value?

(A) 1/(3^2)(5^2)
(B) 2/(3^2)(5^2)
(C) 7/(3^3)(5^2)
(D) 45/(3^3)(5^3)
(E) 75/(3^4)(5^5)

Source :- Question Pack 1.

Hello.

I don't know what is the best way to solving it, but I will try it. <i class="em em-grimacing"></i>

First, since the fractions (A) and (B) has the same denominator, then we have to see the numerators and since 2 > 1, we have that the second fraction is greater than the first one. Option A eliminated.

Now, let's rewrite the last two fractions as follows: $$\left(D\right)\frac{45}{3^3\cdot5^3}=\frac{3^2\cdot5}{3^3\cdot5^3}=\frac{1}{3\cdot5^2}.$$ $$\left(E\right)\frac{75}{3^4\cdot5^5}=\frac{3\cdot5^2}{3^4\cdot5^5}=\frac{1}{3^3\cdot5^3}.$$ Since the numerators of the fractions (D) and (E) are the same, we have to see the denominators.

Now, since the denominator of the fraction (E) is greater than the denominator of the fraction (D), this implies that the fraction (D) is greater than the fraction (E). Option E eliminated.

Now, We only have to see the fractions (B), (C) and (D): $$\left(B\right)\ \ \frac{2}{3^2\cdot5^2}\ \ ;\ \ \left(C\right)\ \frac{7}{3^3\cdot5^2}\ \ ;\ \left(D\right)\ \ \frac{1}{3\cdot5^2}$$ $$\Leftrightarrow\ \ \left(B\right)\ \frac{2}{3}\ \frac{1}{3\cdot5^2}=\frac{2}{3}\left(D\right)\ \ ;\ \ \left(C\right)\ \frac{7}{3^2}\frac{1}{3\cdot5^2}=\frac{7}{9}\left(D\right)\ \ ;\ \left(D\right)\ \ \frac{1}{3\cdot5^2}$$ Finally, since $$\frac{2}{3}<1\ \ \ and\ \ \ \ \frac{7}{9}<1\ \ \ then\ D\ is\ the\ greatest\ number.$$ Therefore, the correct answer is the option D.

I hope it is clear enough.

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alanforde800Maximus: Master | Next Rank: 500 Posts; Posts: 187; Joined: Tue Sep 13, 2016 12:46 am

by alanforde800Maximus » Sun May 27, 2018 5:19 pm

Thank You!! for the inputs from your end.

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by Scott@TargetTestPrep » Tue May 29, 2018 6:42 am

alanforde800Maximus wrote:Which of the following fractions has the greatest value?

(A) 1/(3^2)(5^2)
(B) 2/(3^2)(5^2)
(C) 7/(3^3)(5^2)
(D) 45/(3^3)(5^3)
(E) 75/(3^4)(5^5)

To start, we see that 2/(3^2)(5^2) > 1/(3^2)(5^2), so we can eliminate answer choice A.

Next we can simplify answers D and E.

D) 45/(3^3)(5^3) = (3^2)(5^1)/(3^3)(5^3) = 1/(3^1)(5^2)

E) 75/(3^4)(5^5) = (3^1)(5^2)/(3^4)(5^5) = 1/(3^3)(5^3)

The denominator in E is greater than in D, so we see that D is greater than E, so we can eliminate E. So we are left with:

(B) 2/(3^2)(5^2)

(C) 7/(3^3)(5^2)

(D) 1/(3^1)(5^2)

Getting common denominators we have:

(B) (2)(3^1)/(3^3)(5^2) = 6/(3^3)(5^2)

(C) 7/(3^3)(5^2)

(D) 1(3^2)/(3^3)(5^2) = 9/(3^3)(5^2)

Alternate Solution:

Since answer choices A and B have equal denominators and since B has a greater numerator, B > A.

If we multiply both the numerator and the denominator of B by 3, we obtain 6/(3^3)(5^2). The denominator is equal to the denominator of answer choice C, but the numerator of C is greater; therefore, C > B.

If we multiply both the numerator and the denominator of C by 5, we obtain 35/(3^3)(5^3). The denominator is equal to the denominator of answer choice D, but the numerator of D is greater; therefore, D > C.

Finally, in comparing D and E, we see that if we were to multiply both the numerator and the denominator of D by 3 x 5^2 = 75, we would get a denominator that is equal to the denominator of answer choice E, but the numerator of D, which is 45 x 75, would have been much greater than the numerator of E, which is only 75. Therefore, D > E.

Answer: D

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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by Brent@GMATPrepNow » Tue May 29, 2018 5:48 pm

alanforde800Maximus wrote:Which of the following fractions has the greatest value?

(A) 1/(3^2)(5^2)
(B) 2/(3^2)(5^2)
(C) 7/(3^3)(5^2)
(D) 45/(3^3)(5^3)
(E) 75/(3^4)(5^5)

We might also make things easier by getting rid of the fractions by multiplying all of the values by the lowest common denominator, which is (3^4)(5^5)
let' s do this...

(A) 1/(3^2)(5^2) x (3^4)(5^5) = (3^2)(5^3) = (9)(125)
(B) 2/(3^2)(5^2) x (3^4)(5^5) = (2)(3^2)(5^3) = (2)(9)(125)
(C) 7/(3^3)(5^2) x (3^4)(5^5) = (7)(3^1)(5^3) = (7)(3)(125)
(D) 45/(3^3)(5^3) x (3^4)(5^5) = (45)(3^1)(5^2) = (45)(3)(25)
(E) 75/(3^4)(5^5) x (3^4)(5^5) = 75

We can immediately ELIMINATE A and E

Let's fiddle a bit with B, C and D
We have:
(B) (2)(9)(125)
(C) (7)(3)(125)
(D) (45)(3)(25)

Divide all quantities by 25 to get:
(B) (2)(9)(5)
(C) (7)(3)(5)
(D) (45)(3)

Divide all quantities by 5 to get:
(B) (2)(9)
(C) (7)(3)
(D) (9)(3)

At this point, we can evaluate the values to see that answer choice D is greatest.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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