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18 Feb 2026, 20:00
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
76% (01:48) correct
24%
(02:31)
wrong
based on 58
sessions
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Once all applicants were sorted into groups of 6, for group discussions, 2 were left over. If there were more than 40 but fewer than 70 applicants, how many applicants were there?
(1) If all the applicants had been sorted into groups of 5, there would have been none left over.
(2) If all the applicants had been sorted into groups of 7, there would have been 1 left over.
(1) If all the applicants had been sorted into groups of 5, there would have been none left over.
(2) If all the applicants had been sorted into groups of 7, there would have been 1 left over.
19 Feb 2026, 00:18
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Possible scenarios for applicants= (44,50,56,62,68)
Statement 1: only 50 satisfies. Therefore Sufficient
Statement 2: again only 50 satisfies. Therefore Sufficient
Answer is option (D)
Statement 1: only 50 satisfies. Therefore Sufficient
Statement 2: again only 50 satisfies. Therefore Sufficient
Answer is option (D)
19 Feb 2026, 05:08
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Key Concept: Remainders & Divisibility (Data Sufficiency)
The common trap here is jumping straight to testing numbers without first setting up the remainder constraints systematically. Let me show you the clean approach.
What the question tells us:
Number of applicants N satisfies:
— N ≡ 2 (mod 6), meaning N leaves remainder 2 when divided by 6
— 40 < N < 70
Step 1 — List all values in range satisfying the given condition.
Multiples of 6 between 40 and 70: 42, 48, 54, 60, 66
Add 2 to each: 44, 50, 56, 62, 68
These are your only candidates. Write them down — this is your working set.
Step 2 — Test Statement (1): "If sorted into groups of 5, none left over" → N ≡ 0 (mod 5)
From {44, 50, 56, 62, 68}, which are divisible by 5?
Only 50. Statement (1) alone gives a unique answer. ✅ Sufficient.
Step 3 — Test Statement (2): "If sorted into groups of 7, remainder is 1" → N ≡ 1 (mod 7)
Check each candidate:
44 ÷ 7 = 6 remainder 2 ✗
50 ÷ 7 = 7 remainder 1 ✓
56 ÷ 7 = 8 remainder 0 ✗
62 ÷ 7 = 8 remainder 6 ✗
68 ÷ 7 = 9 remainder 5 ✗
Only 50 works. Statement (2) alone also gives a unique answer. ✅ Sufficient.
Answer: D — each statement alone is sufficient.
The trap to avoid: Some students skip the Step 1 enumeration and try to evaluate the statements in isolation from scratch — that leads to messy algebra and mistakes. Whenever DS gives you a bounded range, your first move should always be to write out the complete candidate list from the original constraint, then filter with each statement.
Takeaway: In DS Remainders questions with a finite range, enumerate all valid candidates first — then each statement becomes a simple filter test.
The common trap here is jumping straight to testing numbers without first setting up the remainder constraints systematically. Let me show you the clean approach.
What the question tells us:
Number of applicants N satisfies:
— N ≡ 2 (mod 6), meaning N leaves remainder 2 when divided by 6
— 40 < N < 70
Step 1 — List all values in range satisfying the given condition.
Multiples of 6 between 40 and 70: 42, 48, 54, 60, 66
Add 2 to each: 44, 50, 56, 62, 68
These are your only candidates. Write them down — this is your working set.
Step 2 — Test Statement (1): "If sorted into groups of 5, none left over" → N ≡ 0 (mod 5)
From {44, 50, 56, 62, 68}, which are divisible by 5?
Only 50. Statement (1) alone gives a unique answer. ✅ Sufficient.
Step 3 — Test Statement (2): "If sorted into groups of 7, remainder is 1" → N ≡ 1 (mod 7)
Check each candidate:
44 ÷ 7 = 6 remainder 2 ✗
50 ÷ 7 = 7 remainder 1 ✓
56 ÷ 7 = 8 remainder 0 ✗
62 ÷ 7 = 8 remainder 6 ✗
68 ÷ 7 = 9 remainder 5 ✗
Only 50 works. Statement (2) alone also gives a unique answer. ✅ Sufficient.
Answer: D — each statement alone is sufficient.
The trap to avoid: Some students skip the Step 1 enumeration and try to evaluate the statements in isolation from scratch — that leads to messy algebra and mistakes. Whenever DS gives you a bounded range, your first move should always be to write out the complete candidate list from the original constraint, then filter with each statement.
Takeaway: In DS Remainders questions with a finite range, enumerate all valid candidates first — then each statement becomes a simple filter test.
