DS: Ratio & Proportion – Level 2
1.
A recipe calls for sugar and flour in a specific ratio. How much sugar is needed?
(1) The ratio of sugar to flour is 2:5.
(2) If 15 cups of flour are used, the recipe is followed correctly.
(1) The ratio of sugar to flour is 2:5.
(2) If 15 cups of flour are used, the recipe is followed correctly.
Solution (C):
Analyze Statement (1): Ratio \(S:F = 2:5\). Without knowing a quantity, we can’t find the amount of sugar. Not Sufficient.
Analyze Statement (2): Flour = 15. Without the ratio, we can’t find sugar. Not Sufficient.
Combine: \(\frac{S}{15} = \frac{2}{5} \implies S=6\). Sufficient.
Analyze Statement (1): Ratio \(S:F = 2:5\). Without knowing a quantity, we can’t find the amount of sugar. Not Sufficient.
Analyze Statement (2): Flour = 15. Without the ratio, we can’t find sugar. Not Sufficient.
Combine: \(\frac{S}{15} = \frac{2}{5} \implies S=6\). Sufficient.
2.
Is \(x > y\)?
(1) The ratio of \(x\) to \(y\) is \(3:2\).
(2) The ratio of \(x\) to \(y\) is \(3:2\) and \(y > 0\).
(1) The ratio of \(x\) to \(y\) is \(3:2\).
(2) The ratio of \(x\) to \(y\) is \(3:2\) and \(y > 0\).
Solution (B):
Analyze Statement (1): \(\frac{x}{y} = 1.5\). If \(y=2, x=3\) (Yes). If \(y=-2, x=-3\) (No, since \(-3 < -2\)). Not Sufficient.
Analyze Statement (2): \(\frac{x}{y} = 1.5\) and \(y > 0\). Since \(y\) is positive and the ratio is positive, \(x\) must be positive. Since the ratio \(>1\), the numerator must be larger than the denominator. \(x > y\). Sufficient.
Analyze Statement (1): \(\frac{x}{y} = 1.5\). If \(y=2, x=3\) (Yes). If \(y=-2, x=-3\) (No, since \(-3 < -2\)). Not Sufficient.
Analyze Statement (2): \(\frac{x}{y} = 1.5\) and \(y > 0\). Since \(y\) is positive and the ratio is positive, \(x\) must be positive. Since the ratio \(>1\), the numerator must be larger than the denominator. \(x > y\). Sufficient.
3.
A box contains green and yellow balls. If 10 green balls are added, what is the new ratio of green to yellow balls?
(1) Originally, there were 20 green and 30 yellow balls.
(2) Originally, the ratio of green to yellow balls was 2:3.
(1) Originally, there were 20 green and 30 yellow balls.
(2) Originally, the ratio of green to yellow balls was 2:3.
Solution (A):
Analyze Statement (1): Original: \(G=20, Y=30\). Add 10 Green \(\to\) New \(G=30, Y=30\). New ratio is 1:1. Sufficient.
Analyze Statement (2): Original ratio \(2:3\). This could mean 20G/30Y (New ratio 30:30=1:1) or 200G/300Y (New ratio 210:300=7:10). Different results. Not Sufficient.
Analyze Statement (1): Original: \(G=20, Y=30\). Add 10 Green \(\to\) New \(G=30, Y=30\). New ratio is 1:1. Sufficient.
Analyze Statement (2): Original ratio \(2:3\). This could mean 20G/30Y (New ratio 30:30=1:1) or 200G/300Y (New ratio 210:300=7:10). Different results. Not Sufficient.
4.
Is the integer \(k\) divisible by 6?
(1) The ratio \(k:6\) is an integer.
(2) The ratio \(k:12\) is an integer.
(1) The ratio \(k:6\) is an integer.
(2) The ratio \(k:12\) is an integer.
Solution (D):
Analyze Statement (1): \(\frac{k}{6} = \text{Integer}\). This literally means \(k\) is a multiple of 6. Yes. Sufficient.
Analyze Statement (2): \(\frac{k}{12} = \text{Integer}\). This means \(k\) is a multiple of 12 (e.g., 12, 24, 36). All multiples of 12 are also multiples of 6. Yes. Sufficient.
Analyze Statement (1): \(\frac{k}{6} = \text{Integer}\). This literally means \(k\) is a multiple of 6. Yes. Sufficient.
Analyze Statement (2): \(\frac{k}{12} = \text{Integer}\). This means \(k\) is a multiple of 12 (e.g., 12, 24, 36). All multiples of 12 are also multiples of 6. Yes. Sufficient.
5.
What is the ratio of \(a:b:c\)?
(1) \(a:b = 1:2\).
(2) \(b:c = 2:3\).
(1) \(a:b = 1:2\).
(2) \(b:c = 2:3\).
Solution (C):
Analyze Statement (1): Relates \(a\) and \(b\), but no info on \(c\). Not Sufficient.
Analyze Statement (2): Relates \(b\) and \(c\), but no info on \(a\). Not Sufficient.
Combine: Since \(b\) is represented by ‘2’ in both ratios, we can combine them directly: \(a:b:c = 1:2:3\). Sufficient.
Analyze Statement (1): Relates \(a\) and \(b\), but no info on \(c\). Not Sufficient.
Analyze Statement (2): Relates \(b\) and \(c\), but no info on \(a\). Not Sufficient.
Combine: Since \(b\) is represented by ‘2’ in both ratios, we can combine them directly: \(a:b:c = 1:2:3\). Sufficient.
Score: 0 / 0