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02 Apr 2025, 10:19
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C
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:
71% (01:34) correct
29%
(01:35)
wrong
based on 191
sessions
History
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Time
Result
Not Attempted Yet
A supermarket holds a promotional lottery, whose winners pick one product from list 1 and one product from list 2 as their prizes. There are a total of 42 possible combinations of products, and no product is present on both lists. How many products are on list 1?
(1) There are more products on list 1 than on list 2.
(2) There are a total of 13 products on the two lists.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statement (1) and (2) TOGETHER are NOT sufficient.
1000012618.jpg [ 567.29 KiB | Viewed 1292 times ]
(1) There are more products on list 1 than on list 2.
(2) There are a total of 13 products on the two lists.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statement (1) and (2) TOGETHER are NOT sufficient.
Attachment:
1000012618.jpg [ 567.29 KiB | Viewed 1292 times ]
24 Apr 2026, 13:35
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Classic Data Sufficiency setup. Let's call the number of products on list 1 as "a" and list 2 as "b."
The question tells us: a * b = 42. We need to find "a."
Factorizations of 42 to consider: 1*42, 2*21, 3*14, 6*7. Without anything else, we can't determine a.
Statement (1): a > b. This narrows things down to (a, b) being (7,6), (14,3), (21,2), or (42,1). Multiple options, so not sufficient.
Statement (2): a + b = 13. Combined with a * b = 42, we get a quadratic: n^2 - 13n + 42 = 0, which factors as (n-6)(n-7) = 0. So a = 6 or a = 7. Still two options -- we don't know which list is list 1 and which is list 2. Not sufficient alone.
(1) + (2) together: a + b = 13, a * b = 42, and a > b. From statement 2 we know {a, b} = {6, 7}. Since a > b, we get a = 7. Sufficient.
Answer: C.
The trap in this one is thinking statement 2 alone is sufficient because it pins down the two numbers as 6 and 7. But "sufficient" for Data Sufficiency means we can determine a unique value for list 1 specifically -- and statement 2 alone doesn't tell us which of the two lists is the bigger one.
The question tells us: a * b = 42. We need to find "a."
Factorizations of 42 to consider: 1*42, 2*21, 3*14, 6*7. Without anything else, we can't determine a.
Statement (1): a > b. This narrows things down to (a, b) being (7,6), (14,3), (21,2), or (42,1). Multiple options, so not sufficient.
Statement (2): a + b = 13. Combined with a * b = 42, we get a quadratic: n^2 - 13n + 42 = 0, which factors as (n-6)(n-7) = 0. So a = 6 or a = 7. Still two options -- we don't know which list is list 1 and which is list 2. Not sufficient alone.
(1) + (2) together: a + b = 13, a * b = 42, and a > b. From statement 2 we know {a, b} = {6, 7}. Since a > b, we get a = 7. Sufficient.
Answer: C.
The trap in this one is thinking statement 2 alone is sufficient because it pins down the two numbers as 6 and 7. But "sufficient" for Data Sufficiency means we can determine a unique value for list 1 specifically -- and statement 2 alone doesn't tell us which of the two lists is the bigger one.
25 Apr 2026, 01:20
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Fast solve.
Given:
a × b = 42
So possible pairs:
(42,1), (21,2), (14,3), (7,6)
From statement (1):
a > b
So possible:
(42,1), (21,2), (14,3), (7,6)
Still multiple → not sufficient
---
From statement (2):
a + b = 13
So possible:
(7,6) or (6,7)
---
Now combine (1) and (2):
a > b and a + b = 13
So only:
(7,6)
Hence,
a = 7
Final Answer: C
Hope this helps—feel free to upvote if useful.
If you have similar questions, tag me—I’ll try to help.
— Rajdeep
Given:
a × b = 42
So possible pairs:
(42,1), (21,2), (14,3), (7,6)
From statement (1):
a > b
So possible:
(42,1), (21,2), (14,3), (7,6)
Still multiple → not sufficient
---
From statement (2):
a + b = 13
So possible:
(7,6) or (6,7)
---
Now combine (1) and (2):
a > b and a + b = 13
So only:
(7,6)
Hence,
a = 7
Final Answer: C
Hope this helps—feel free to upvote if useful.
If you have similar questions, tag me—I’ll try to help.
— Rajdeep
