If (a – b) : (b – c) : (c – d) : (d – e) = 1 : 2 : 3 : 6, then what is

Question

If (a – b) : (b – c) : (c – d) : (d – e) = 1 : 2 : 3 : 6, then what is the value of (a + e)/d ?

(A) 2/7
(B) 2/5
(C) 3/5
(D) 2/3
(E) 2/1

chetan2u · Accepted Answer

As we are talking of ratios, let us assume some values for each.  
(a – b) : (b – c) : (c – d) : (d – e) = 1 : 2 : 3 : 6

Let the common ratio be 1, so  
If e is 0, d-e=6 or d=6
c-d=3, so c=9
b-c=2, so b=12
a-b=1, so a=12

\frac{a-e}{d}=\frac{12-0}{6}=\frac{2}{1}

E

LaveenaPanchal · Answer

Let a-b=x, so b = a-x 
b-c=2x, so c = b - 2x
c-d=3x so d = c-3x
d-e=6x so e = d-6x

e = d-6x = c-3x-6x = b-2x-9x = a-x-11x = a-12x
d = c-3x = b - 2x-3x = b-5x = a-x-5x = a-6x
 (a+e) / d = (a + a -12x)/a-6x = 2a-12x/a-6x = 2(a-6x)/a-6x = 2/1

Answer is E.

Navnit99 · Answer

I have a different approach for this question.

(a – b) : (b – c) : (c – d) : (d – e) = 1 : 2 : 3 : 6

(a – b) is positive that means a>b
similarly b>c, c>d and d>e

therefore a is biggest number and e is smallest of all and d is somewhere between a and e. 
Now (a+e)/d must be greater then one, and only one option is greater than one. that is option E

If (a – b) : (b – c) : (c – d) : (d – e) = 1 : 2 : 3 : 6, then what is

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If (a – b) : (b – c) : (c – d) : (d – e) = 1 : 2 : 3 : 6, then what is

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