DS: Ratio & Proportion – Level 1
Directions: Choose the correct option (A-E) based on sufficiency.
1.
What is the ratio of boys to girls in the class?
(1) There are 15 boys in the class.
(2) There are 20 girls in the class.
(1) There are 15 boys in the class.
(2) There are 20 girls in the class.
Solution (C):
Analyze Statement (1): Gives number of boys (\(B=15\)). We don’t know the number of girls. Not Sufficient.
Analyze Statement (2): Gives number of girls (\(G=20\)). We don’t know the number of boys. Not Sufficient.
Combine: We have \(B=15\) and \(G=20\). Ratio = \(15:20 = 3:4\). Sufficient.
Analyze Statement (1): Gives number of boys (\(B=15\)). We don’t know the number of girls. Not Sufficient.
Analyze Statement (2): Gives number of girls (\(G=20\)). We don’t know the number of boys. Not Sufficient.
Combine: We have \(B=15\) and \(G=20\). Ratio = \(15:20 = 3:4\). Sufficient.
2.
If \(x\) and \(y\) are positive numbers, what is the value of \(y\)?
(1) The ratio \(x:y\) is \(2:3\).
(2) \(x = 10\).
(1) The ratio \(x:y\) is \(2:3\).
(2) \(x = 10\).
Solution (C):
Analyze Statement (1): \(\frac{x}{y} = \frac{2}{3}\). Infinite possibilities (e.g., \(x=2, y=3\) or \(x=4, y=6\)). Not Sufficient.
Analyze Statement (2): \(x = 10\). No info on \(y\). Not Sufficient.
Combine: \(\frac{10}{y} = \frac{2}{3} \implies 2y = 30 \implies y = 15\). Sufficient.
Analyze Statement (1): \(\frac{x}{y} = \frac{2}{3}\). Infinite possibilities (e.g., \(x=2, y=3\) or \(x=4, y=6\)). Not Sufficient.
Analyze Statement (2): \(x = 10\). No info on \(y\). Not Sufficient.
Combine: \(\frac{10}{y} = \frac{2}{3} \implies 2y = 30 \implies y = 15\). Sufficient.
3.
Are there more red marbles than blue marbles in the jar?
(1) The ratio of red marbles to blue marbles is \(5:4\).
(2) There are 45 marbles in total.
(1) The ratio of red marbles to blue marbles is \(5:4\).
(2) There are 45 marbles in total.
Solution (A):
Analyze Statement (1): Ratio \(R:B = 5:4\). Since \(5 > 4\), regardless of the multiplier, there will always be more red marbles. (e.g., 5R/4B, 10R/8B). Sufficient.
Analyze Statement (2): Total = 45. Could be 1 Red/44 Blue (No) or 44 Red/1 Blue (Yes). Not Sufficient.
Analyze Statement (1): Ratio \(R:B = 5:4\). Since \(5 > 4\), regardless of the multiplier, there will always be more red marbles. (e.g., 5R/4B, 10R/8B). Sufficient.
Analyze Statement (2): Total = 45. Could be 1 Red/44 Blue (No) or 44 Red/1 Blue (Yes). Not Sufficient.
4.
What is the value of \(a\)?
(1) \(a\) is to \(b\) as \(3\) is to \(4\).
(2) \(b = 20\) and the ratio of \(a\) to \(b\) is \(1:5\).
(1) \(a\) is to \(b\) as \(3\) is to \(4\).
(2) \(b = 20\) and the ratio of \(a\) to \(b\) is \(1:5\).
Solution (B):
Analyze Statement (1): \(\frac{a}{b} = \frac{3}{4}\). We don’t know \(b\), so we can’t find \(a\). Not Sufficient.
Analyze Statement (2): \(b=20\) and \(\frac{a}{b} = \frac{1}{5}\). So \(\frac{a}{20} = \frac{1}{5} \implies a = 4\). Sufficient.
Analyze Statement (1): \(\frac{a}{b} = \frac{3}{4}\). We don’t know \(b\), so we can’t find \(a\). Not Sufficient.
Analyze Statement (2): \(b=20\) and \(\frac{a}{b} = \frac{1}{5}\). So \(\frac{a}{20} = \frac{1}{5} \implies a = 4\). Sufficient.
5.
What is the ratio of apples to oranges in the basket?
(1) There are 10 apples.
(2) There are 15 bananas.
(1) There are 10 apples.
(2) There are 15 bananas.
Solution (E):
Analyze Statement (1): Knowing only apples tells us nothing about oranges. Not Sufficient.
Analyze Statement (2): Knowing bananas tells us nothing about apples or oranges. Not Sufficient.
Combine: We know apples=10, bananas=15. We still don’t know the number of oranges. Not Sufficient.
Analyze Statement (1): Knowing only apples tells us nothing about oranges. Not Sufficient.
Analyze Statement (2): Knowing bananas tells us nothing about apples or oranges. Not Sufficient.
Combine: We know apples=10, bananas=15. We still don’t know the number of oranges. Not Sufficient.
Score: 0 / 0