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Difficulty:
95%
(hard)
Question Stats:
37% (03:20) correct
63%
(03:09)
wrong
based on 63
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X is a three-digit number whose hundredth digit, tens digit, and units digit are in arithmetic progression and in ascending order. Find the ratio of its middle digit and common difference.
(1) The sum of the products of the digits taken two at a time is 11/3 times the product of its extreme digits
(2) The product of the sum of its digits taken two at a time is 10 times the product of its digits.
(1) The sum of the products of the digits taken two at a time is 11/3 times the product of its extreme digits
(2) The product of the sum of its digits taken two at a time is 10 times the product of its digits.
sobby
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26 Nov 2016, 10:27
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AR15J
Although i got the answer but solving the equation took more that 3.5 minutes.
...It will be easy if we select number as x-a , x , x+a....
28 Nov 2016, 02:41
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Hi Sobby,
It will be very difficult and tedious to use numbers to satisfy the given statements in this question. Remember you will need to get at least two to three examples to check if the statements are sufficient or not. The best method to solve this problem is to use variables which are in an Arithmetic Progression (ascending order) for the hundredth, tens and units digit. Now before we jump the gun and use three variables in AP x, x + a and x + 2a, we first need to glance at the statements. Both the statements deal with products and sums of the three variables. It would be wiser to use the three variables as x - a, x and x + a as the hundreds, tens and units digit respectively.
The question here is a value DS question where we now need to find the ratio of x : a.
Statement 1 : The sum of the products of the digits taken two at a time is 11/3 times the product of its extreme digits
(x-a)(x) + (x)(x+a) + (x-a)(x+a) = (11/3)(x-a)(x+a)
Expanding the terms and simplifying we get 3x^2 - a^2 = (11/3)(x^2 - a^2) ------> 4a^2 = x^2 -----> x/a = 2/1. Sufficient.
Statement 2 : The product of the sum of its digits taken two at a time is 10 times the product of its digits.
(x-a+x)(x-a+x+a)(x+x+a) = 10(x-a)(x)(x+a)
Expanding the terms and simplifying we get (4x^2 - a^2) (2x) = 10(x)(x^2 - a^2) ------> 2x^3 = 8xa^2 -----> x/a = 2/1.
OA : D
CrackVerbal Academics Team
It will be very difficult and tedious to use numbers to satisfy the given statements in this question. Remember you will need to get at least two to three examples to check if the statements are sufficient or not. The best method to solve this problem is to use variables which are in an Arithmetic Progression (ascending order) for the hundredth, tens and units digit. Now before we jump the gun and use three variables in AP x, x + a and x + 2a, we first need to glance at the statements. Both the statements deal with products and sums of the three variables. It would be wiser to use the three variables as x - a, x and x + a as the hundreds, tens and units digit respectively.
The question here is a value DS question where we now need to find the ratio of x : a.
Statement 1 : The sum of the products of the digits taken two at a time is 11/3 times the product of its extreme digits
(x-a)(x) + (x)(x+a) + (x-a)(x+a) = (11/3)(x-a)(x+a)
Expanding the terms and simplifying we get 3x^2 - a^2 = (11/3)(x^2 - a^2) ------> 4a^2 = x^2 -----> x/a = 2/1. Sufficient.
Statement 2 : The product of the sum of its digits taken two at a time is 10 times the product of its digits.
(x-a+x)(x-a+x+a)(x+x+a) = 10(x-a)(x)(x+a)
Expanding the terms and simplifying we get (4x^2 - a^2) (2x) = 10(x)(x^2 - a^2) ------> 2x^3 = 8xa^2 -----> x/a = 2/1.
OA : D
CrackVerbal Academics Team
