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05 Feb 2026, 22:47
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Difficulty:
95%
(hard)
Question Stats:
41% (02:23) correct
59%
(02:18)
wrong
based on 93
sessions
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The median age of 7 children in group A was 13. The median age of 9 children in group B was 9. Four children – the youngest and the oldest in each group – were exchanged between the groups. What was the new median age of the children in group B?
(1) Before the exchange, the oldest child in group B was 12 years old.
(2) Before the exchange, the youngest child in group A was 8 years old.
(1) Before the exchange, the oldest child in group B was 12 years old.
(2) Before the exchange, the youngest child in group A was 8 years old.
06 Feb 2026, 00:36
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This is a classic median manipulation problem! The key is understanding what actually changes when we swap the extreme values.
Step 1: Set up what we know initially
Group A has 7 children with median 13 → the 4th child (middle position) is 13 years old.
Group B has 9 children with median 9 → the 5th child (middle position) is 9 years old.
Step 2: Understand the exchange
After swapping the youngest and oldest from each group, Group B will have 9 children total (we removed 2 and added 2). The new median will still be the 5th position when ordered.
Step 3: Analyze Statement (1)
Statement (1): The oldest child in group B was 12 before the exchange.
This tells us Group B lost a 12-year-old (the oldest). But we don't know what age children Group B gained from Group A. Since Group A's median was 13, the oldest child in Group A could be 13 or higher. We know Group A's youngest was exchanged, but we don't know that age either.
Not sufficient on its own.
Step 4: Analyze Statement (2)
Statement (2): The youngest child in group A was 8 before the exchange.
This tells us Group B gained an 8-year-old. But we don't know what Group B lost (we don't know the ages of Group B's youngest or oldest children).
Not sufficient on its own.
Step 5: Combine both statements
From (1): Group B lost its oldest child (12) and youngest child (unknown age)
From (2): Group B gained an 8-year-old and gained Group A's oldest child (at least 13)
Here's the critical insight: Group B's original median was 9, meaning at least 5 children were ≤9. Since we removed the oldest (12) and the youngest, and added an 8 and someone ≥13, we're essentially replacing two values without knowing the original youngest of Group B. We still can't definitively determine the new 5th position.
Wait—let me reconsider. Actually, knowing the original youngest of B would help. But we're not told that. Combined, we know B lost 12 and gained 13+, and gained 8, but without knowing B's original youngest, we can't determine the new median.
Answer: E (both together insufficient)
Common trap: Many students pick C, thinking the information combines nicely. The trap is forgetting that we need to know Group B's original youngest age to determine how the ordered list changes. Data Sufficiency is all about what's provable, not what seems reasonable!
Takeaway: On median problems with exchanges, always track which positions in the ordered set are affected. The median only changes if values near the middle position change—knowing the extremes isn't always enough.
Step 1: Set up what we know initially
Group A has 7 children with median 13 → the 4th child (middle position) is 13 years old.
Group B has 9 children with median 9 → the 5th child (middle position) is 9 years old.
Step 2: Understand the exchange
After swapping the youngest and oldest from each group, Group B will have 9 children total (we removed 2 and added 2). The new median will still be the 5th position when ordered.
Step 3: Analyze Statement (1)
Statement (1): The oldest child in group B was 12 before the exchange.
This tells us Group B lost a 12-year-old (the oldest). But we don't know what age children Group B gained from Group A. Since Group A's median was 13, the oldest child in Group A could be 13 or higher. We know Group A's youngest was exchanged, but we don't know that age either.
Not sufficient on its own.
Step 4: Analyze Statement (2)
Statement (2): The youngest child in group A was 8 before the exchange.
This tells us Group B gained an 8-year-old. But we don't know what Group B lost (we don't know the ages of Group B's youngest or oldest children).
Not sufficient on its own.
Step 5: Combine both statements
From (1): Group B lost its oldest child (12) and youngest child (unknown age)
From (2): Group B gained an 8-year-old and gained Group A's oldest child (at least 13)
Here's the critical insight: Group B's original median was 9, meaning at least 5 children were ≤9. Since we removed the oldest (12) and the youngest, and added an 8 and someone ≥13, we're essentially replacing two values without knowing the original youngest of Group B. We still can't definitively determine the new 5th position.
Wait—let me reconsider. Actually, knowing the original youngest of B would help. But we're not told that. Combined, we know B lost 12 and gained 13+, and gained 8, but without knowing B's original youngest, we can't determine the new median.
Answer: E (both together insufficient)
Common trap: Many students pick C, thinking the information combines nicely. The trap is forgetting that we need to know Group B's original youngest age to determine how the ordered list changes. Data Sufficiency is all about what's provable, not what seems reasonable!
Takeaway: On median problems with exchanges, always track which positions in the ordered set are affected. The median only changes if values near the middle position change—knowing the extremes isn't always enough.
06 Feb 2026, 05:37
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Statement (2) alone is sufficient and the new median of Group B remains 9.
Let the ages in Group B be ordered as b1, b2, b3, b4, b5, b6, b7, b8, b9, with median b5 = 9. After removing the youngest and the oldest children from Group B, we are left with b2 through b8. In this ordered list of 7 values, the middle (4th) value is still b5, which is 9.
From statement (2), the youngest child in Group A is 8, which is less than 9. Since the median of Group A is 13, the oldest child in Group A must be at least 13, which is greater than 9. When we add 8 (below 9) and the oldest child from Group A (above 9) to Group B, the value 9 shifts back to the 5th position in the new ordered list of 9 children. Therefore, the median of Group B remains 9.
Statement (1) alone is not sufficient.
Answer: B.
Let the ages in Group B be ordered as b1, b2, b3, b4, b5, b6, b7, b8, b9, with median b5 = 9. After removing the youngest and the oldest children from Group B, we are left with b2 through b8. In this ordered list of 7 values, the middle (4th) value is still b5, which is 9.
From statement (2), the youngest child in Group A is 8, which is less than 9. Since the median of Group A is 13, the oldest child in Group A must be at least 13, which is greater than 9. When we add 8 (below 9) and the oldest child from Group A (above 9) to Group B, the value 9 shifts back to the 5th position in the new ordered list of 9 children. Therefore, the median of Group B remains 9.
Statement (1) alone is not sufficient.
Answer: B.
