Question:
A set \(S\) contains 12 consecutive integers. The sum of the 6 smallest integers of \(S\) is 321. The mean of the largest six integers of \(S\) is
A set \(S\) contains 12 consecutive integers. The sum of the 6 smallest integers of \(S\) is 321. The mean of the largest six integers of \(S\) is
Show Hint
The mean of consecutive integers equals the average of the first and last terms.
Updated On: Jun 15, 2026
- 59.5
- 62.5
- 64.2
- 65.8
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Let the smallest integer be \(n\).
Then the six smallest integers are
\[
n,n+1,n+2,n+3,n+4,n+5.
\]
Their sum is
\[
6n+15=321
\]
\[
6n=306
\]
\[
n=51.
\]
Thus the 12 integers are
\[
51,52,53,\ldots,62.
\]
The largest six integers are
\[
57,58,59,60,61,62.
\]
Their mean is
\[
\frac{57+58+59+60+61+62}{6}
\]
\[
=\frac{357}{6}
\]
\[
=59.5.
\]
Was this answer helpful?
0
0
Top TG ICET Mathematical Ability Questions
- \[ \frac{\left(a^{\frac12}b^{-\frac16}\right)^3- \left(a^{\frac16}b^{\frac13}\right)^3} {a^{\frac12}-b^{\frac12}} = ? \]
- \[ 64^{\frac13} - 81^{\frac14} + 625^{\frac14} = ? \]
- If \(x:y=4:5\), then \((5x+4y):(10x-2y)=\ ?\)
- The ratio of milk and water in a can of 36 liters is \(3:1\). If 6 more liters of water is added, then the ratio of the milk and water will be:
- If \[ \sqrt{12+4\sqrt5} + \sqrt{16-4\sqrt7} = \sqrt{x}+\sqrt{y}, \] then find the value of \[ \sqrt{35xy}. \]
View More Questions
Top TG ICET Statistics Questions
- The lines $3x-2y=-6$ and $x+y=3$ meet the $Y$-axis at the point $A$ and meet the $X$-axis at the points $B$ and $C$. Then the area of $\triangle ABC$ (in sq. units) is
- If the line $5y=7x$ divides the line segment joining the points $(3,5)$ and $(-5,2)$ in the ratio $m:n$ (where $\gcd(m,n)=1$), then the least value of $m^{2}+n^{2}$ is}
- If the angle between the lines $7x+3py+5=0$ and $3x-14py+11=0$ is $\frac{\pi}{2}$, then a value of $p$ is}
- If \(m\) and \(c\) denote the slope and the \(y\)-intercept of the line \(3x-5y-6=0\), then \((m,c)=\)
- If the equation of the line passing through the point \((-4,3)\) and having a slope \(\left(-\frac{2}{3}\right)\) is \(ax+by=c\), then \(a^2+b^2-c^2=\)
View More Questions
Top TG ICET Questions
- What is the average of the integers 1, 2, 3, 4, and \(x\)? Statement (I): \(x\) is an even integer. Statement (II): \(x<10\)
- What is the average of \(x,y,z\) and \(t\)? Statement (I): \(x+z=12\) Statement (II): \(y+t=24\)
- What is the sum of the first 30 terms of an Arithmetic Progression? Statement (I): The common difference of the A.P. is 5. Statement (II): The first and the last terms are 2 and 60 respectively.
- In triangle \(ABC\), is \(\angle A\) obtuse? Statement (I): \(\angle C\) is acute. Statement (II): \(\angle B\) is obtuse.
- What is the circumference of the regular hexagon? Statement (I): The radius of the circumcircle of the hexagon is \(6\) cm. Statement (II): Each side of the hexagon subtends an angle of \(60^\circ\) at the centre.
View More Questions