DS: Percentage – Level 1
1.
What is the value of \(x\)?
(1) 40% of \(x\) is 20.
(2) 50% of \(x\) is 25.
(1) 40% of \(x\) is 20.
(2) 50% of \(x\) is 25.
Solution (D):
Analyze Statement (1): \(0.40x = 20\). We can solve for \(x\): \(x = 20 / 0.4 = 50\). Since we found a unique value, this is Sufficient.
Analyze Statement (2): \(0.50x = 25\). We can solve for \(x\): \(x = 25 / 0.5 = 50\). Since we found a unique value, this is Sufficient.
Conclusion: Since each statement alone provided the answer, the correct choice is D.
Analyze Statement (1): \(0.40x = 20\). We can solve for \(x\): \(x = 20 / 0.4 = 50\). Since we found a unique value, this is Sufficient.
Analyze Statement (2): \(0.50x = 25\). We can solve for \(x\): \(x = 25 / 0.5 = 50\). Since we found a unique value, this is Sufficient.
Conclusion: Since each statement alone provided the answer, the correct choice is D.
2.
Is \(y\) greater than 30?
(1) \(y\) is 25% of \(z\).
(2) \(z\) is equal to 100.
(1) \(y\) is 25% of \(z\).
(2) \(z\) is equal to 100.
Solution (C):
Analyze Statement (1): \(y = 0.25z\). Without knowing the value of \(z\), we cannot determine the value of \(y\). It could be anything. Not Sufficient.
Analyze Statement (2): \(z = 100\). This tells us about \(z\), but gives no relationship to determine \(y\). Not Sufficient.
Combine (1) and (2): Substitute \(z=100\) into the first equation: \(y = 0.25(100) = 25\). Now we can answer the question: Is \(25 > 30\)? No. We have a definitive answer. Sufficient.
Analyze Statement (1): \(y = 0.25z\). Without knowing the value of \(z\), we cannot determine the value of \(y\). It could be anything. Not Sufficient.
Analyze Statement (2): \(z = 100\). This tells us about \(z\), but gives no relationship to determine \(y\). Not Sufficient.
Combine (1) and (2): Substitute \(z=100\) into the first equation: \(y = 0.25(100) = 25\). Now we can answer the question: Is \(25 > 30\)? No. We have a definitive answer. Sufficient.
3.
What is the value of \(x\)?
(1) \(x\) is 50% of \(y\).
(2) \(y\) is 200% of \(x\).
(1) \(x\) is 50% of \(y\).
(2) \(y\) is 200% of \(x\).
Solution (E):
Analyze Statement (1): \(x = 0.5y\). This is a linear equation with two variables. \(x\) could be 1 (if \(y=2\)) or 100 (if \(y=200\)). Not Sufficient.
Analyze Statement (2): \(y = 2.0x\). If we divide by 2, we get \(0.5y = x\). This is mathematically identical to Statement (1). It provides no new information. Not Sufficient.
Combine (1) and (2): Since both statements tell us the same relative relationship (\(y=2x\)) but give no actual numbers, we still cannot find the specific value of \(x\). Not Sufficient.
Analyze Statement (1): \(x = 0.5y\). This is a linear equation with two variables. \(x\) could be 1 (if \(y=2\)) or 100 (if \(y=200\)). Not Sufficient.
Analyze Statement (2): \(y = 2.0x\). If we divide by 2, we get \(0.5y = x\). This is mathematically identical to Statement (1). It provides no new information. Not Sufficient.
Combine (1) and (2): Since both statements tell us the same relative relationship (\(y=2x\)) but give no actual numbers, we still cannot find the specific value of \(x\). Not Sufficient.
4.
Is \(p\) greater than 200?
(1) 10% of \(p\) is 25.
(2) 20% of \(p\) is greater than 10.
(1) 10% of \(p\) is 25.
(2) 20% of \(p\) is greater than 10.
Solution (A):
Analyze Statement (1): \(0.10p = 25 \implies p = 250\). Is \(250 > 200\)? Yes. We have a definite answer. Sufficient.
Analyze Statement (2): \(0.20p > 10 \implies p > 50\). If \(p\) is 51, the answer is No. If \(p\) is 250, the answer is Yes. Since we get multiple possibilities, this is Not Sufficient.
Analyze Statement (1): \(0.10p = 25 \implies p = 250\). Is \(250 > 200\)? Yes. We have a definite answer. Sufficient.
Analyze Statement (2): \(0.20p > 10 \implies p > 50\). If \(p\) is 51, the answer is No. If \(p\) is 250, the answer is Yes. Since we get multiple possibilities, this is Not Sufficient.
5.
What is the value of \(n\)?
(1) \(n\) is a positive integer.
(2) 150% of \(n\) is 45.
(1) \(n\) is a positive integer.
(2) 150% of \(n\) is 45.
Solution (B):
Analyze Statement (1): \(n\) could be 1, 2, 3… Infinite possibilities. Not Sufficient.
Analyze Statement (2): \(1.5n = 45 \implies n = 45 / 1.5 = 30\). We found a unique numerical value. Sufficient.
Analyze Statement (1): \(n\) could be 1, 2, 3… Infinite possibilities. Not Sufficient.
Analyze Statement (2): \(1.5n = 45 \implies n = 45 / 1.5 = 30\). We found a unique numerical value. Sufficient.
Score: 0 / 0