If an exam has 1.5 points for a correct answer and -0.4 for a wrong answer, calculate the expected value of a random guess if there are 5 possible options.

The probability of choosing the correct answer is $\frac{1}{5} = 0.2$ and the probability of a wrong answer is $\frac{4}{5} = 0.8$. The expected value is $(0.2 \times 1.5) + (0.8 \times -0.4) = 0.3 - 0.32 = -0.02$. Since the expected value is negative, random guessing is statistically disadvantageous.

Given 44 heads and 132 legs, determine the number of four-legged animals (H) and two-legged creatures (C) using the system of equations.

Use the system: $C + H = 44$ $2C + 4H = 132$ Multiply the first by 2: $2C + 2H = 88$. Subtract from the second: $2H = 44$, so $H = 22$. Substituting back: $C = 22$. There are 22 four-legged animals and 22 two-legged creatures.

Balance the chemical equation: a $C_3H_8 + b O_2 \rightarrow c CO_2 + d H_2O$.

Using atomic balances: Carbon: $3a = c$ Hydrogen: $8a = 2d \Rightarrow 4a = d$ Oxygen: $2b = 2c + d$ Set $a=1$: $c=3$, $d=4$. Then $2b = 2(3) + 4 = 10$, so $b=5$. The balanced equation is $C_3H_8 + 5O_2 \rightarrow 3CO_2 + 4H_2O$.

Calculate the percentage decrease if a value drops from 80 to 60.

The change is $80 - 60 = 20$. The percentage decrease is calculated as $\frac{Change}{Original} \times 100 = \frac{20}{80} \times 100 = 0.25 \times 100 = 25\%$.

Determine the force required to accelerate a 5kg mass from rest to $10\,m/s$ in $2\,s$.

First, find acceleration: $a = \frac{v - u}{t} = \frac{10 - 0}{2} = 5\,m/s^2$. Then, use Newton's second law: $F = ma = 5\,kg \times 5\,m/s^2 = 25\,N$.

If 17.5% of a population of 800 people have a specific trait, calculate the total number of people using component percentages .

Break 17.5% into 10% + 5% + 2.5%: 10% of 800 = 80 5% of 800 = 40 2.5% of 800 = 20 Total = $80 + 40 + 20 = 140$.

Identify the logical flaw in the argument: 'My doctor is healthy and eats apples, therefore eating apples makes you healthy.'

The argument commits the error of correlation vs causation . It assumes that because two factors (eating apples and health) occur together, one must cause the other, while ignoring other variables like exercise, genetics, or lifestyle.

Calculate the final velocity of an object dropped from rest after falling for 4 seconds, assuming $g = 9.8\,m/s^2$.

Using the kinematic equation $v = u + at$: $v = 0 + (9.8\,m/s^2 \times 4\,s) = 39.2\,m/s$.

Find the area of a circle inscribed in a square with side length 4.

If the side of the square is 4, the diameter of the inscribed circle is 4, so the radius $r = 2$. The area $A = \pi r^2 = \pi (2)^2 = 4\pi$.

Determine the probability of rolling a sum of 4 with two fair six-sided dice.

The possible outcomes for a sum of 4 are (1,3), (2,2), and (3,1). There are 3 successful outcomes out of $6 \times 6 = 36$ total possibilities. The probability is $\frac{3}{36} = \frac{1}{12}$.

Simplify the expression $\frac{x^2 - 9}{x+3}$.

Recognize the numerator as a difference of squares : $x^2 - 3^2 = (x-3)(x+3)$. Therefore, $\frac{(x-3)(x+3)}{x+3} = x - 3$ (for $x \neq -3$).

Calculate the total resistance of two $6\,\Omega$ resistors connected in parallel.

For resistors in parallel, $\frac{1}{R_t} = \frac{1}{R_1} + \frac{1}{R_2}$. Thus, $\frac{1}{R_t} = \frac{1}{6} + \frac{1}{6} = \frac{2}{6} = \frac{1}{3}$. Therefore, $R_t = 3\,\Omega$.

Explain how to identify an unstated assumption in a reading passage.

An assumption is a premise that must be true for the conclusion to follow logically, even if it is not explicitly mentioned. Test for it by asking: 'If this specific statement were proven false, would the conclusion still be supported by the premises?' If the argument collapses, that statement is a necessary assumption.

Calculate the power dissipated by a resistor with $I = 2\,A$ and $V = 10\,V$.

Using the formula $P = IV$: $P = 2\,A \times 10\,V = 20\,W$.

If a substance has a half-life of 10 years, how much of a 100g sample remains after 30 years?

The substance undergoes 3 half-lives ($30 / 10 = 3$): After 10 years: 50g After 20 years: 25g After 30 years: 12.5g The remaining amount is 12.5g.

Essential Problem Solving And Science Foundations For The Imat Exam Flashcards

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Essential Problem Solving and Science Foundations for the IMAT Exam

This deck focuses on core logical reasoning, mathematical problem-solving strategies, and scientific principles required for success in the IMAT entrance examination.

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by @rabia_arshad

Q: If an exam has 1.5 points for a correct answer and -0.4 for a wrong answer, calculate the ex...

Q: Given 44 heads and 132 legs, determine the number of four-legged animals (H) and <s...

Q: Balance the chemical equation: a $C_3H_8 + b O_2 \rightarrow <stro...

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