Aptitude - Problems on Numbers - Discussion

First mutiple 11* -70 which gives product = -770 and sum = 13.

Next factorise 770 number ,u will get 2*5*7*11...in this series try to make combination such that sum should be 13 and product should be -770.

The combination which we get is by trial and error, is 5*7=35 and 2*11=22, hence we choose 35 and -22 to satisfy p=-770 and sum=13,

Next substitute in equation,
11x^2+35x-22x+4=0.
x(11x+35)-2(11x+35)=0.

Hence,
(x-2)(11x+35) = 0.
Hence we get x = 2 and y = x+2 = 4.

Dear experts,

Please solve the following problem:

In a two-digit, if it is known that its unit's digit exceeds its ten's digit by 2 and if 18 is added with the number then the digits exchanges their position. Find the number with explanation.

Here's the answer 24, but I need algebraic explanation. Thanks.

Multiply a term(11) and c term (-70) = -770.

Find two numbers that when multiplied equal the number (-770) and add up to be the b term (13).

The numbers be -22 and 35.

Now write this as,

11x2-22x+35x-70 = 0.

11x (x-2) +35 (x-2) = 0.

The factors are x-2 and 11x-35.

If I'm wrong, please explain me.

@All.

Here, I completely disagree.

The problem indicates in a two-digit if it is known that its unit's digit exceeds its ten's digit by 2. None of the answers presented are for example 31 or 42 , 53 or 64....etc. etc,

The answer of 24, is incorrect within the rule of the question.

@Ayushi.

=(11x+2)(2x+2)=144 (Multiplication with both values 11x => 2x & 2 and 2 => 2x & 2).

=>22x^2+22x+4x+4 = 144,
22x^2+26x+4-144 = 0,
22x^2+26x-140=0/squaring this value.
11x2 + 13x - 70 = 0.
We get.
(x - 2)(11x + 35) = 0,
x = 2.

The simple method is to check the option.

Options B and C are wrong because of their option B] difference is not 2 and option C] unit digit is greater than 2. So this is neglected.

Now remaining option is 24 checks it 24 * (2 + 4) = 144 is true then it's a right answer.

Let the ten's digit be x.

Then, unit's digit = x + 2.

for Example: Take Number 56.

Here unit digit is 6, ten's digit is 5, Then Number = 50(since its 10th digit)+6 = 56.

Hence in the above case: Number = 10x+ (x+2) = 11x+2.

The remaining same explained by indiabix.

Its not the case of confusing..its the case of time consuming...just check the options only two options may give the answer..24 and 46... now apply the second condition given in the problenm to these two options

24*(2+4)=144.. so this is the correct answer

@All.

If the 10th place be denoted by 10x then unit place exceeds 2 more than the 10th place then unit place value should be denoted as 10x+2 why they denote x+2 for the unit place. Please explain this.

In the question it is clearly mentioned that units digit is 2 more than tens digit, then by observing the options only in 24 units digit(i.e.4 ) is more than 2 with tens digit(i.e.2).