If A, B, C and D are positive integers such that 4A = 9B, 17C = 11D

Question

If A, B, C and D are positive integers such that 4A = 9B, 17C = 11D, and 5C = 12A, then the arrangement of the four numbers from greatest to least is

A. CDAB
B. BACD
C. DCAB
D. DCBA
E. BDAC

pushpitkc · Accepted Answer

4A = 9B -> A = 9B/4 If B=4, A=9 - Hence,  A>B 
5C = 12A -> A = 5C/12 If C=12,A=5 - Hence,  C>A 
17C = 11D -> C = 11D/17 If D=17, C=11 - Hence,  D>C

Hence D > C, C > A and A > B

So, the sequence should be D,C,A and B(Option C)

kumarparitosh123 · Answer

From equation 1 , A=9/4B,
From equation 3, A=5/12C,
From equation 3, C=11/17D.
On solving all we get
A=9/4B=5/12C=55/204D

WHICH FINALLY YIELDS
204A=459B=85C=55D.

THUS B IS GREATEST AN ANSWER IS BACD. OPTION B

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kumarparitosh123 · Answer

My bad !! I took it totally opposite. I need to be careful in real exam for such mistakes. 
Thanks pushpit. Your solutions at amazing.

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generis · Answer

pushpitkc  , I think you have a typo that throws off your subsequent analysis and has you adding what I think is an unnecessary step.

Initially you write:

But then you write:

Then you revert back to A > B while comparing B and C.

I'm pretty sure there is no need to compare B and C. (See my solution below.)

C > A, A > B, hence C > B.

I might be missing something.

generis · Answer

If 4A = 9B:

A =  \frac{9}{4} B

B =  \frac{4}{9} A

A > B

If 17C = 11D

C =  \frac{11}{17} D

D =  \frac{17}{11} C

D > C

If 5C = 12A

C =  \frac{12}{5} A

A =  \frac{5}{12} C

C > A 
_____
THUS
 A > B
D > C
 C > A

If you're tracking on C (greater than A and B), you'll remember that you discovered D > C, and you are done. D>C>A>B. Or:

From last and first inequalities we know 
C > A, and 
A > B, so

We have C > A > B.

Anything bigger than C? From second inequality, D > C.

Hence D>C>A>B

Answer C

P.S. In three or four inequalities such as those above, if a variable shows up only once on LHS or RHS, it's either the biggest or the smallest. So you can look for the variables that show up once and work from greatest to least or vice versa. You'd see B and D here. If B, ask: anything smaller? No. It's the smallest. If D, ask: anything larger? No. It's the largest. You can either work in order from there or take biggest and smallest and figure out relationship of middle two.

HUNTdGMAT · Answer

Approximately
A= 10/4B or A= 2.5 B
C=10/20D OR C=.5D 
C=10/5A or C=2A
DCAB IS THE ANSWER

Abhibarua · Answer

Is it absolutely necessary to solve the equations? No.

A, B, C, D are positive integers (given)

4A = 9B (which means  A > B )
17C = 11D ( D > C )
5C = 12A ( C> A )

So,  D > C > A > B  (Option: C)

sanya2711 · Answer

a:b:c:d= 495:220:1188:1838
thus, the answer is DCAB

bumpbot · Answer

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If A, B, C and D are positive integers such that 4A = 9B, 17C = 11D

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If A, B, C and D are positive integers such that 4A = 9B, 17C = 11D

Prep Toolkit

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My Rewards