Greatest value?

[bhumika.k.shah]

Which of the following fractions has the greatest value?


A.3 / 8!

B.6*(4!) / 5*(9!)

C.4*(3!) / 9!

D.3 / 5*(7!)

E.14 / 5*(8!)

Quicker and new approaches required.

Source : MGMAT QBANK

[harshavardhanc]

Which of the following fractions has the greatest value?


A.3 / 8!

B.6*(4!) / 5*(9!)

C.4*(3!) / 9!

D.3 / 5*(7!)

E.14 / 5*(8!)

Quicker and new approaches required.

Source : MGMAT QBANK

make all the denominators same ( make them 9!) and then compare the fractions.

[gmatmachoman]

Which of the following fractions has the greatest value?


A.3 / 8!

B.6*(4!) / 5*(9!)

C.4*(3!) / 9!

D.3 / 5*(7!)

E.14 / 5*(8!)

Quicker and new approaches required.

Source : MGMAT QBANK

IS it B?

[bhumika.k.shah]

IS it B?

Nopes

[bhumika.k.shah]

[spoiler]OA D

Each fraction's denominator contains a factorial. Since any smaller factorial divides any larger factorial, any of the factorials smaller than 9! can be multiplied by appropriate terms. (For instance, multiplying 7! by yields 9!.) Therefore, the common denominator of all the fractions is 5(9!).

In (A) the numerator and denominator must be multiplied by 5 × 9; in (C), by 5; in (D), by 8 × 9; and in (E), by 9. No multiplication is necessary in (B).

The fractions now look like this:

(A)
3 × 9 × 5 / 5(9!)

=135 / 5(9!)

(B)
6 × 4 × 3 × 2 × 1/ 5(9!)

= 144 / 5(9!)

(C)
4 × 3 × 2 × 1 × 5/ 5(9!)

= 120/ 5(9!)

(D) 3 × 8 × 9/ 5(9!)

= 216 /5(9!)

(E) 14 × 9 / 5(9!)

= 126 / 5(9!)

Now that the denominators are all the same, we can directly compare the numerators. 216 is the largest numerator.

The correct answer is D.[/spoiler]

[gmatmachoman]

[spoiler]OA D

Each fraction's denominator contains a factorial. Since any smaller factorial divides any larger factorial, any of the factorials smaller than 9! can be multiplied by appropriate terms. (For instance, multiplying 7! by yields 9!.) Therefore, the common denominator of all the fractions is 5(9!).

In (A) the numerator and denominator must be multiplied by 5 × 9; in (C), by 5; in (D), by 8 × 9; and in (E), by 9. No multiplication is necessary in (B).

The fractions now look like this:

(A)
3 × 9 × 5 / 5(9!)

=135 / 5(9!)

(B)
6 × 4 × 3 × 2 × 1/ 5(9!)

= 144 / 5(9!)

(C)
4 × 3 × 2 × 1 × 5/ 5(9!)

= 120/ 5(9!)

(D) 3 × 8 × 9/ 5(9!)

= 216 /5(9!)

(E) 14 × 9 / 5(9!)

= 126 / 5(9!)

Now that the denominators are all the same, we can directly compare the numerators. 216 is the largest numerator.

The correct answer is D.[/spoiler]

I tried this whole problme in my mind.. It was confusing ....!!
Sorry Bhumika for bugging u like anything!!

But atlast I got D!!

[harshavardhanc]

Which of the following fractions has the greatest value?


A.3 / 8!

B.6*(4!) / 5*(9!)

C.4*(3!) / 9!

D.3 / 5*(7!)

E.14 / 5*(8!)

Quicker and new approaches required.

Source : MGMAT QBANK

make all the denominators same ( make them 9!) and then compare the fractions.

so, we have to compare

3*9 , (6*24)/5 , (4*6) , (3*8*9)/5 , and (14*9)/5

or 27, 24, (6*24)/5, (3*8*9)/5 , and (14*9)/5

first compare : (6*24)/5, (3*8*9)/5 , and (14*9)/5

= (24*6)/5, (24*9)/5 , and (14*9)/5

The middle one :(24*9)/5 is greatest.


Now decide : which one is greater (24*9)/5 or 27 ? Or (9* 4.something) or (9*3) ?


hence, Ans : D

[gmatmachoman]

@Harsha Bhai,
Can u try this prblm without using pen/Paper.. & that too in 1 min??

[harshavardhanc]

@Harsha Bhai,
Can u try this prblm without using pen/Paper.. & that too in 1 min??

certainly not !

Buddy, to tell you I only think on paper because whenever i have tried to solve questions in my mind, I've always got an incorrect answer. I'm really a "slow head"

[sanju09]

@Harsha Bhai,
Can u try this prblm without using pen/Paper.. & that too in 1 min??

we'll do the circus later, for now the problem is fixed in no more than the ideal 2 minutes

[sanju09]

@Harsha Bhai,
Can u try this prblm without using pen/Paper.. & that too in 1 min??

certainly not !

Buddy, to tell you I only think on paper because whenever i have tried to solve questions in my mind, I've always got an incorrect answer. I'm really a "slow head"

Same here, I have in point of fact divided my brain in two parts, LEFT and RIGHT. In the LEFT part, there's nothing RIGHT, and in the RIGHT part, there's nothing LEFT

[harshavardhanc]

Same here, I have in point of fact divided my brain in two parts, LEFT and RIGHT. In the LEFT part, there's nothing RIGHT, and in the RIGHT part, there's nothing LEFT

ROFL

[sanju09]

@Harsha Bhai,
Can u try this prblm
Same here, I have in point of fact divided my brain in two parts, LEFT and RIGHT. In the LEFT part, there's nothing RIGHT, and in the RIGHT part, there's nothing LEFT

ROFL

congrats Govind, we're 3 now

[kstv]

A.3 / 8! B.6*(4!) / 5*(9!) C.4*(3!) / 9! D.3 / 5*(7!) E.14 / 5*(8!)
Since the job is to find the max value compairing will yield the result with minimum calculation.
A and E both have 8! in the denominator (D) multiply by 5 the numerator (N) of A will be 15 , N of E = 14
B and C both have 9! in the denominator (D) multiply by 5 the N of B = 6! and C 5!
A 15/8! and B 6!/9! D 15/7! obvious that D is > A as (N) is the same
between B and D - am still doing it mentally.

[sanju09]

A.3 / 8! B.6*(4!) / 5*(9!) C.4*(3!) / 9! D.3 / 5*(7!) E.14 / 5*(8!)
Since the job is to find the max value compairing will yield thhe result with minimum calculation.
A and E both have 8! in the denominator (D) multiply by 5 the numerator (N) of A will be 15 , N of B = 14
B and C both have 9! in the denominator (D) multiply by 5 the N of B = 6! and C 5!
A 15/8! and B 6!/9! D 15/7! obvious that D is > A as (N) is the same
between B and D - am still doing it mentally.

but, we've caught you typing some great sense here, rock u