We are given that the product of three integers X, Y, and Z is 192.
$ X \times Y \times Z = 192 $
We know that Z = 4. Substituting this value:
$ X \times Y \times 4 = 192 $
Divide both sides by 4 to find the product of X and Y:
$ X \times Y = \frac{192}{4} $
$ X \times Y = 48 $
We are also given that P is the average of X and Y:
$ P = \frac{X + Y}{2} $
To find the minimum possible value of P, we need to find the minimum possible value of the sum $(X + Y)$, given that $(X \times Y = 48)$.
Since the options provided are positive values, we consider positive integer pairs for X and Y whose product is 48. We look for the pair with the smallest sum.
Finding Minimum Sum (X + Y)
List the pairs of positive integers (X, Y) whose product is 48 and calculate their sum:
- (1, 48): Sum = $(1 + 48) = 49$
- (2, 24): Sum = $(2 + 24) = 26$
- (3, 16): Sum = $(3 + 16) = 19$
- (4, 12): Sum = $(4 + 12) = 16$
- (6, 8): Sum = $(6 + 8) = 14$
The minimum sum $(X + Y)$ among these pairs is 14, which occurs when X=6 and Y=8 (or vice versa).
Calculating Minimum P
Now, use the minimum sum to calculate the minimum value of P:
$ P_{min} = \frac{min(X + Y)}{2} $
$ P_{min} = \frac{14}{2} $
$ P_{min} = 7 $
Therefore, the minimum possible value of P is 7.
Important Questions from Numerical Reasoning
- Let $p_1$ and $p_2$ denote two arbitrary prime numbers. Which one of the following statements is correct for all values of $p_1$ and $p_2$?
- A 'frabjous' number is defined as a 3 digit number with all digits odd, and no two adjacent digits being the same. For example, 137 is a frabjous number, while 133 is not. How many such frabjous numbers exist?
Ankita has to climb 5 stairs starting at the ground, while respecting the following rules:
1. At any stage, Ankita can move either one or two stairs up.
2. At any stage, Ankita cannot move to a lower step.
Let $F(N)$ denote the number of possible ways in which Ankita can reach the $N^{th}$ stair. For example, $F(1) = 1$, $F(2) = 2$, $F(3) = 3$. The value of $F(5)$ is ________.- In a zoo, three lions and four tigers eat 390 kg of food every week. In another zoo, four lions and five tigers eat 500 kg of food every week. Lions and tigers eat different amounts of food, but all individuals of the same species eat the same amount. The amount of food a single lion eats per week is ________ kg.
(Answer in integer) Consider a spherical globe rotating about an axis passing through its poles. There are three points P, Q, and R situated respectively on the equator, the north pole, and midway between the equator and the north pole in the northern hemisphere. Let P, Q, and R move with speeds $v_P$, $v_Q$, and $v_R$, respectively.
Which one of the following options is CORRECT?
