Register

CAT 2024 Set-1 | Quantitative Aptitude | Question: 8

• edited by
388 views
0 0 votes

Let $x, y$, and $z$ be real numbers satisfying

$\begin{array}{l}  4\left(x^{2}+y^{2}+z^{2}\right)=a, \\ 4(x-y-z)=3+a. \end{array} $

Then $a$ equals

  1. $1 \frac{1}{3}$
  2. $1$
  3. $3$
  4. $4$

Please log in or register to answer this question.

Voting & Accepting an answer helps improve the community
← PreviousNext →
← Previous in categoryNext in category →

Related questions

0 0 votes
0 0 answers
521
521 views
Shubham Sharma 2 asked Jun 26, 2025
521 views
CAT 2024 Set-1 | Quantitative Aptitude | Question: 1
Two places $\text{A}$ and $\text{B}$ are $45$ $\textrm{kms}$ apart and connected by a straight road. Anil goes from $\text{A}$ to $\text{B}$ while Sunil goes from $\text{...
0 0 votes
0 0 answers
419
419 views
Shubham Sharma 2 asked Jun 26, 2025
419 views
CAT 2024 Set-1 | Quantitative Aptitude | Question: 2
Consider two sets $A=\{2,3,5,7,11,13\}$ and $B=\{1,8,27\}$. Let $f$ be a function from $A$ to $B$ such that for every element $b$ in $B$, there is at least one element $a...
0 0 votes
0 0 answers
484
484 views
Shubham Sharma 2 asked Jun 26, 2025
484 views
CAT 2024 Set-1 | Quantitative Aptitude | Question: 3
$\mathrm{ABCD}$ is a rectangle with sides $\text{AB}=56 \mathrm{~cm}$ and $\text{BC}=45 \mathrm{~cm}$, and $\text{E}$ is the midpoint of side $\text{CD}$. Then, the lengt...
0 0 votes
0 0 answers
415
415 views
Shubham Sharma 2 asked Jun 26, 2025
415 views
CAT 2024 Set-1 | Quantitative Aptitude | Question: 4
In September, the incomes of Kamal, Amal and Vimal are in the ratio $8: 6: 5$. They rent a house together, and Kamal pays $15 \%$, Amal pays $12 \%$ and Vimal pays $18 \%...
0 0 votes
0 0 answers
382
382 views
Shubham Sharma 2 asked Jun 26, 2025
382 views
CAT 2024 Set-1 | Quantitative Aptitude | Question: 5
Suppose $x_{1}, x_{2}, x_{3}, \ldots, x_{100}$ are in arithmetic progression such that $x_{5}=-4$ and $2 x_{6}+2 x_{9}=x_{11}+x_{13}$. Then, $x_{100}$ equals$206$$204$$-1...