Question : Three numbers are such that the average of the first two numbers is 2, the average of the last two numbers is 3 and the average of the first and last number is 4, then the average of the three numbers is equal to:
Option 1: 2
Option 2: 3.5
Option 3: 3
Option 4: 2.5
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Correct Answer: 3
Solution : Let the three numbers be $x,y,$ and $z$. The average of the first two numbers is 2. $⇒x+y=2×2=4$ The average of the last two numbers is 3 and the average of the first and last numbers is 4. $⇒y+z=2×3=6$ $⇒x+z=2×4=8$ Adding the above equations, we get, $2(x+y+z)=18$ $\therefore (x+y+z)=9$ So, the average of three numbers $=\frac{(x+y+z)}{3}=\frac{9}{3}=3$ Hence, the correct answer is 3.
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Question : Three numbers are such that the average of the first two numbers is 2, the average of the last two numbers is 3 and the average of the first and the last numbers is 4. What is the average of the three numbers?
Question : Among three numbers, the first is twice the second and thrice the third. If the average of these three numbers is 396, then what is the difference between the first and the third number?
Option 1: 594
Option 2: 448
Option 3: 432
Option 4: 453
Question : Two positive whole numbers are such that the sum of the first number and twice the second number is 8, and their difference is 2. The numbers are:
Option 1: 7 and 5
Option 2: 6 and 4
Option 3: 4 and 2
Option 4: 3 and 5
Question : Six numbers are arranged in decreasing order. The average of the first five numbers is 30, and the average of the last five numbers is 25. The difference between the first and last numbers is:
Option 1: 20
Option 2: 25
Option 3: 5
Option 4: 30
Question : The sum of the two numbers is 520. If the bigger number is decreased by 4% and the smaller number is increased by 12%, then the numbers obtained are equal. The smaller number is:
Option 1: 280
Option 2: 210
Option 3: 240
Option 4: 300
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