These are sample practice MCQs created for exam preparation. These are NOT official exam questions.
The set {3, 8, 10, 15, x} has a median of 10. If x is an integer, how many possible values can x have?
Question:
The set {3, 8, 10, 15, x} has a median of 10. If x is an integer, how many possible values can x have?
The set {3, 8, 10, 15, x} has a median of 10. If x is an integer, how many possible values can x have?
Options
Answer: (E) Infinitely many
Explanation:
For median to be 10 with 5 numbers, the middle (3rd) value must be 10. Current ordered values with unknown x position: if x ≤ 10, order could be {3, 8, 10, 15, x} or variations. For median = 10, we need 10 to be the 3rd value when ordered. This works when x ≥ 10 (giving {3, 8, 10, 15, x} or {3, 8, 10, x, 15}) or when x ≤ 8 (giving {x, 3, 8, 10, 15} or {3, x, 8, 10, 15}). But we need exactly 10 as median. If x ≤ 10: {3, 8, x, 10, 15} or {3, 8, 10, x, 15}. For median = 10, middle value is 3rd position. When x ≥ 10: {3, 8, 10, x, 15} - median is 10 ✓. So x can be any integer ≥ 10, giving infinitely many values.
Explanation:
For median to be 10 with 5 numbers, the middle (3rd) value must be 10. Current ordered values with unknown x position: if x ≤ 10, order could be {3, 8, 10, 15, x} or variations. For median = 10, we need 10 to be the 3rd value when ordered. This works when x ≥ 10 (giving {3, 8, 10, 15, x} or {3, 8, 10, x, 15}) or when x ≤ 8 (giving {x, 3, 8, 10, 15} or {3, x, 8, 10, 15}). But we need exactly 10 as median. If x ≤ 10: {3, 8, x, 10, 15} or {3, 8, 10, x, 15}. For median = 10, middle value is 3rd position. When x ≥ 10: {3, 8, 10, x, 15} - median is 10 ✓. So x can be any integer ≥ 10, giving infinitely many values.
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