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# Of the following expressions, which one has the smallest value?

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Director
Joined: 12 Feb 2015
Posts: 917
Of the following expressions, which one has the smallest value?  [#permalink]

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01 Feb 2019, 11:33
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Difficulty:

65% (hard)

Question Stats:

39% (01:45) correct 61% (01:38) wrong based on 44 sessions

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Of the following expressions, which one has the smallest value?

A) $$\frac{2 (3^2)}{7^2}$$

B) $$\frac{10 (3^2)}{7^3}$$

C) $$\frac{5 (3^3)}{7^3}$$

D) $$\frac{100 (3^2)}{7^4}$$

E) $$\frac{25 (3^3)}{7^4}$$

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Manish

"Only I can change my life. No one can do it for me"
Director
Joined: 09 Mar 2018
Posts: 996
Location: India
Of the following expressions, which one has the smallest value?  [#permalink]

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Updated on: 02 Feb 2019, 11:01
CAMANISHPARMAR wrote:
Of the following expressions, which one has the smallest value?

A) $$\frac{2 (3^2)}{7^2}$$

B) $$\frac{10 (3^2)}{7^3}$$

C) $$\frac{5 (3^3)}{7^3}$$

D) $$\frac{100 (3^2)}{7^4}$$

E) $$\frac{25 (3^3)}{7^4}$$

IMO B

After been unsuccessful at ballpark , inline is an old school approach(as suggested by OP)

Lets make all the options have the same base

A) $$\frac{2 (3^2)}{7^2}$$

$$\frac{49 (18)}{7^4}$$

B) $$\frac{10 (3^2)}{7^3}$$

$$\frac{70 (3^2)}{7^4}$$ -> Only B will have the smallest numerator, making this the smallest value

C) $$\frac{5 (3^3)}{7^3}$$

$$\frac{35 (3^3)}{7^4}$$

D) $$\frac{100 (3^2)}{7^4}$$

E) $$\frac{25 (3^3)}{7^4}$$
_________________
If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.

Originally posted by KanishkM on 01 Feb 2019, 20:25.
Last edited by KanishkM on 02 Feb 2019, 11:01, edited 1 time in total.
Manager
Joined: 11 Dec 2013
Posts: 121
Location: India
GMAT Date: 03-15-2015
WE: Education (Education)
Re: Of the following expressions, which one has the smallest value?  [#permalink]

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01 Feb 2019, 22:52
1
As $$\frac{3^2}{7^2}$$ is common in all the options , remove it and compare the rest
A) $$2$$
B) $$\frac{10}{7}$$
C) $$\frac{15}{7} > 2$$
D) $$\frac{100}{49} > 2$$
E) $$\frac{75}{49}$$

Only need to check between B and E
$$\frac{10}{7}$$ = 1.4
$$\frac{75}{49}$$ = 1.5

IMO B
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Of the following expressions, which one has the smallest value?  [#permalink]

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Updated on: 03 Feb 2019, 11:58
1
1
KanishkM wrote:
CAMANISHPARMAR wrote:
Of the following expressions, which one has the smallest value?

A) $$\frac{2 (3^2)}{7^2}$$

B) $$\frac{10 (3^2)}{7^3}$$

C) $$\frac{5 (3^3)}{7^3}$$

D) $$\frac{100 (3^2)}{7^4}$$

E) $$\frac{25 (3^3)}{7^4}$$

IMO ( i ball parked the values for the 1st time,lets wait for the OA now )

18/49 ~ 1/3

90/343 ~ 1/4

135/343 ~ 1/2 < x < 1/3 ~ 0.39

900/2401 ~ 1/2 < x < 1/3 ~ 0.36

225/2401 ~ 1/10 < x < 1/11

It should be between C and D

C

You may like to try once again with some strategy rather than brutal math

What if you mutiply the numerator and denomenator by 7 for option A and compare A, B & C first; Once you have a common denominator, compare only the numerators of these 3 options to select the smallest value. Again multiply the num and deno of this one selected option by 7 and compare only the numerator of the selected option with D & E, to get the right ans. Also maintain 7^3 in first step and 7^4 in the second...no need to calculate these values. Similarly maintain 3^2 in the numerator seperate in all the 5 options as its common to all.

Should not take more than 2 minutes

All the best!!
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Manish

"Only I can change my life. No one can do it for me"

Originally posted by CAMANISHPARMAR on 02 Feb 2019, 10:43.
Last edited by CAMANISHPARMAR on 03 Feb 2019, 11:58, edited 2 times in total.
Manager
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Location: India
Concentration: Finance, Entrepreneurship
GMAT 1: 710 Q49 V38
GPA: 4
Re: Of the following expressions, which one has the smallest value?  [#permalink]

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02 Feb 2019, 11:29
CAMANISHPARMAR wrote:
Of the following expressions, which one has the smallest value?

A) $$\frac{2 (3^2)}{7^2}$$

B) $$\frac{10 (3^2)}{7^3}$$

C) $$\frac{5 (3^3)}{7^3}$$

D) $$\frac{100 (3^2)}{7^4}$$

E) $$\frac{25 (3^3)}{7^4}$$

Easiest way to do is take out the common factor and forget about it

Common factor is:3^2/7^2

So,
A=2
B=10/7 (slightly less than 1.5)
C=5*3/7 (>2)
D=100/49 (>2)
E=25*3/49 (slightly more than 1.5)

_________________

GMAT:710 (Q49,V38,IR8,AWA5)
Re: Of the following expressions, which one has the smallest value?   [#permalink] 02 Feb 2019, 11:29
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