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

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

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New post 01 Feb 2019, 11:33
3
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A
B
C
D
E

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

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New post 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) \(\frac{25 (3^3)}{7^4}\)
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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.
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Re: Of the following expressions, which one has the smallest value?  [#permalink]

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New post 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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New post Updated on: 03 Feb 2019, 11:58
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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 :lol: )

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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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.
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Re: Of the following expressions, which one has the smallest value?  [#permalink]

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New post 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)

So, Answer:B
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Re: Of the following expressions, which one has the smallest value?   [#permalink] 02 Feb 2019, 11:29
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