search
Log In
Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true
1 vote
44 views

Consider the pair of equations: $x^{2} – xy – x = 22$ and $y^{2} – xy + y = 34.$ If $x>y,$ then $x – y$ equals

  1. $7$
  2. $8$
  3. $6$
  4. $4$
in Quantitative Aptitude 2.7k points 5 79 342
retagged by
44 views

1 Answer

1 vote

Given that,  

  • $x^{2} – yx – x = 22\quad \longrightarrow(1)$
  • $y^{2} – xy + y = 34\quad \longrightarrow(2)$
  • $x>y$

From equation $(1),$

$x^{2} – yx – x = 22$

$\Rightarrow x(x-y-1) = 22\quad \longrightarrow(3)$

From equation $(2),$

$y^{2} – xy + y = 34$

$\Rightarrow y(y-x+1) = 34$

Multiply $‘-’$ on both the sides.

$-y(y-x+1) = -34$

$\Rightarrow y(-y+x-1) = -34$

$\Rightarrow y(x-y-1) = -34\quad \longrightarrow(4)$

Subtract equation $(4),$ from equation $(3).$ 

$ x(x-y-1) - y(x-y-1) = 22-(-34)$

$\Rightarrow (x-y-1)(x-y) = 56 \quad \longrightarrow(5)$

Let, $x-y = m \quad  {\color{Blue} {(x>y \Rightarrow  x – y >0 \Rightarrow m>0)}}$

Now, $(m-1)m = 56$

$\Rightarrow m^{2}-m-56 =0$

$\Rightarrow m^{2}-8m+7m-56 =0$

$\Rightarrow m(m-8)+7(m-8) =0$

$\Rightarrow (m-8)(m+7) =0$

$\Rightarrow m=8\; \text{(or)}\; m=-7\;{\color{Red} {\text{(rejected)}}}$

$\Rightarrow \boxed{m=8}$

$\Rightarrow \boxed{x-y=8}$

Correct Answer $:\text{B}$

10.1k points 4 8 30
edited by
Answer:

Related questions

1 vote
1 answer
1
74 views
Anil, Bobby and Chintu jointly invest in a business and agree to share the overall profit in proportion to their investments. Anil's share of investment is $70 \%.$ His share of profit decreases by $₹ \; 420$ if the overall profit goes down from $18 \%$ to $15 \%.$ Chintu's share of ... goes up from $15 \%$ to $17 \%.$ The amount, $\text{in INR},$ invested by Bobby is $2400$ $2200$ $2000$ $1800$
asked Jan 20 in Quantitative Aptitude soujanyareddy13 2.7k points 5 79 342 74 views
1 vote
1 answer
2
82 views
If a rhombus has area $12 \; \text{sq cm}$ and side length $5 \; \text{cm},$ then the length, $\text{in cm},$ of its longer diagonal is $\sqrt{13} + \sqrt{12}$ $\sqrt{37} + \sqrt{13}$ $\frac{\sqrt{37} + \sqrt{13}}{2}$ $\frac{\sqrt{13} + \sqrt{12}}{2}$
asked Jan 20 in Quantitative Aptitude soujanyareddy13 2.7k points 5 79 342 82 views
1 vote
1 answer
3
73 views
The number of ways of distributing $15$ identical balloons, $6$ identical pencils and $3$ identical erasers among $3$ children, such that each child gets at least four balloons and one pencil, is
asked Jan 20 in Quantitative Aptitude soujanyareddy13 2.7k points 5 79 342 73 views
1 vote
1 answer
4
68 views
For a sequence of real numbers $x_{1}, x_{2}, \dots , x_{n},$ if $x_{1} – x_{2} + x_{3} – \dots + (-1)^{n+1} x_{n} = n^{2} + 2n$ for all natural numbers $n,$ then the sum $x_{49} + x_{50}$ equals $2$ $-2$ $200$ $-200$
asked Jan 20 in Quantitative Aptitude soujanyareddy13 2.7k points 5 79 342 68 views
1 vote
1 answer
5
47 views
For a real number $x$ the condition $|3x – 20| + |3x – 40| = 20$ necessarily holds if $9 < x < 14$ $6 < x < 11$ $7 < x < 12$ $10 < x < 15$
asked Jan 20 in Quantitative Aptitude soujanyareddy13 2.7k points 5 79 342 47 views
...