GATE EC 2016 Set 3 Q3 — General Aptitude

The statements (S$1$), (S$2$), and (S$3$) pertain to the scores obtained by students in an exam. The maximum possible marks in the exam is $150$. (S$1$) The highest score is $100$. (S$2$) The fourth highest score is $76$. (S$3$) There are at least four students whose scores are within $25$ of each other. Which one of the following options …

Real numbers $y, p$, and $n$ (all greater than $1$ ) satisfy $$\left(\log _{p^{1 / n}} y\right)\left(\log _{y^{1 / n}} p\right)=16$$ where the logarithms are taken to the bases $p^{1 / n}$ and $y^{1 / n}$. The value of $n$ is $\_\_\_\_$

The following observation is made about the scores obtained by $100$ students in an exam: 'For each student, there exists another student in the class such that their scores are at most ten marks away.' If the above statement is false, which one of the following statements is necessarily true?

Three children $\mathrm{P}, \mathrm{Q}, \mathrm{R}$ and two grown-ups $\mathrm{X}, \mathrm{Y}$ play a badminton doubles tournament. $\text{X}$ and $\text{Y}$ are parents to two of the children playing. The child of $\text{X}$ is not the same as the child of $\text{Y}.$ Exactly one of the children does not have a parent playing in the tournament. …

Let $P_{k}$ represent the perimeter of a square with sides of length $k$. The value of the expression $P_{1}+P_{2}+P_{3}+\cdots+P_{10}$ is $\_\_\_\_$

The city of Atlantis was crafted by the God of the seas, Poseidon. It was made of alternating concentric circular rings of land (shaded) and water (not shaded) as represented in the figure (not to scale). The radius of Inner Island was $2.5$ stades (a unit of length used in ancient Greece). The water surrounding Inner Island was one stade wide (length AB …