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11 Jun 2025, 09:58
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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0% (00:00) correct
100% (02:23) wrong based on 1 sessions
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Set A consists of 35 consecutive integers.
Quantity A
The probability of selecting an even number less than the median from set A
Quantity B
The probability of selecting an odd number greater than the median from set A
Quantity A
The probability of selecting an even number less than the median from set A
Quantity B
The probability of selecting an odd number greater than the median from set A
17 Jun 2025, 01:04
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Given: Set A consists of 35 consecutive integers.
To Compare:
Solution:
Step 1: Median of Set A
Step 2: Numbers less than the median:
Step 3: Numbers greater than the median:
Notice that for any n:
So, there is no consistent relationship.
Correct Answer: (D)
Shweta Koshija
GMAT, GRE, SAT Coach for 10+ years
To Compare:
- Quantity A — Probability of picking an even number less than the median
- Quantity B — Probability of picking an odd number greater than the median
Solution:
Step 1: Median of Set A
- In 35 consecutive integers, median = 18th number.
- Let Set A = {n, n+1, n+2, ..., n+34}
- Then, median = n+17.
Step 2: Numbers less than the median:
- These are n to n+16 — 17 numbers in total.
- Among these 17 numbers, either 8 or 9 will be even depending on whether n is odd or even:
- If n is even, there will be 9 even numbers.
- If n is odd, there will be 8 even numbers.
- So possible values for Quantity A numerator = 8 or 9.
- Hence, Quantity A can be 9/35 or 8/35.
Step 3: Numbers greater than the median:
- These are n+18 to n+34 — again 17 numbers.
- Similarly, the number of odd numbers here will also be 8 or 9.
- If n is even, there will be 8 odd numbers.
- If n is odd, there will be 9 odd numbers.
- So possible values for Quantity B numerator = 8 or 9.
- Hence, Quantity A can be 8/35 or 9/35.
Notice that for any n:
- If Quantity A = 9/35, then Quantity B = 8/35 (A > B)
- If Quantity A = 8/35, then Quantity B = 9/35 (A > B)
So, there is no consistent relationship.
Correct Answer: (D)
Shweta Koshija
GMAT, GRE, SAT Coach for 10+ years
19 Jun 2025, 12:00
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OE
In a set of 35 consecutive integers, the median will be the number in the middle. Of the remaining 34 values, 17 will be less than the median and 17 will be
greater.
Imagine that the range of values is 1 through 35. In this case, the first value is odd, and the values 1 through 17 are below the median, 18 is the median, and 19 through 35 are above the median. So there are 9 odd numbers and 8 even numbers below the median, the median itself is even, and there are 9 odd numbers and 8 even numbers above the median.
Now imagine that the range of values is 2 through 36. In this case, the first value is even, the median is 19, there are 9 even numbers and 8 odd numbers below the median, and there are 9 even numbers and 8 odd numbers above the median.
So, if the first integer is odd, there’s an 8 in 35 chance of picking an even number less than the median and a 9 in 35 chance of picking an odd number greater than the median. Quantity B would be greater than Quantity A. However, if the first integer is even, the odds are reversed, with a 9 in 35 chance of picking an even number less than the median and an 8 in 35 chance of picking an odd number greater than the median. That would make Quantity A greater than Quantity B. Because more than one relationship is possible, (D) is the correct answer.
Answer: D
In a set of 35 consecutive integers, the median will be the number in the middle. Of the remaining 34 values, 17 will be less than the median and 17 will be
greater.
Imagine that the range of values is 1 through 35. In this case, the first value is odd, and the values 1 through 17 are below the median, 18 is the median, and 19 through 35 are above the median. So there are 9 odd numbers and 8 even numbers below the median, the median itself is even, and there are 9 odd numbers and 8 even numbers above the median.
Now imagine that the range of values is 2 through 36. In this case, the first value is even, the median is 19, there are 9 even numbers and 8 odd numbers below the median, and there are 9 even numbers and 8 odd numbers above the median.
So, if the first integer is odd, there’s an 8 in 35 chance of picking an even number less than the median and a 9 in 35 chance of picking an odd number greater than the median. Quantity B would be greater than Quantity A. However, if the first integer is even, the odds are reversed, with a 9 in 35 chance of picking an even number less than the median and an 8 in 35 chance of picking an odd number greater than the median. That would make Quantity A greater than Quantity B. Because more than one relationship is possible, (D) is the correct answer.
Answer: D
