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14 Feb 2026, 01:21
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
28% (02:04) correct
72%
(02:25)
wrong
based on 68
sessions
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Not Attempted Yet
At a certain store, each soft drink costs d dollars, and each cookie costs c dollars. If Mario has enough money for 4 soft drinks and 2 cookies, does he also have enough money for 4 cookies and two soft drinks?
(1) Mario has enough money for 3 cookies and 3 soft drinks.
(2) Mario has enough money for 6 cookies.
(1) Mario has enough money for 3 cookies and 3 soft drinks.
(2) Mario has enough money for 6 cookies.
14 Feb 2026, 02:01
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This is a clever Data Sufficiency problem that tests whether you can translate word problems into algebra and spot the hidden comparison.
Let M = Mario's total money
What we know:[b] M ≥ 4d + 2c (he can afford 4 soft drinks and 2 cookies)
[b]What we need to know:[b] Is M ≥ 4c + 2d? (Can he afford 4 cookies and 2 soft drinks?)
Here's the key insight: We're really asking whether 4c + 2d ≤ 4d + 2c
Simplifying: 2c ≤ 2d, or [b]c ≤ d[b]
So the entire question boils down to: Are cookies cheaper than or equal to soft drinks?
[b]Statement (1): Mario has enough money for 3 cookies and 3 soft drinks[b]
M ≥ 3c + 3d = 3(c + d)
We already know M ≥ 4d + 2c. Does this tell us whether c ≤ d?
Try c = $2, d = $3: Then 4d + 2c = $16, and 3c + 3d = $15. If M = $16, both conditions work. Is c ≤ d? Yes (2 ≤ 3), so he CAN afford 4c + 2d = $14.
Try c = $3, d = $2: Then 4d + 2c = $14, and 3c + 3d = $15. If M = $15, both conditions work. Is c ≤ d? No (3 > 2), so 4c + 2d = $16, which exceeds his money.
[b]NOT SUFFICIENT[b]
[b]Statement (2): Mario has enough money for 6 cookies[b]
M ≥ 6c
This tells us nothing about d. We can't compare c and d.
[b]NOT SUFFICIENT[b]
[b]Combined (1) + (2):[b]
From (1): M ≥ 3c + 3d
From (2): M ≥ 6c
Given: M ≥ 4d + 2c
Using the same number tests from Statement (1), even with both statements we still can't determine whether c ≤ d. The statements give us bounds on M, but not the price relationship we need.
[b]STILL NOT SUFFICIENT[b]
[b]Answer: E[b]
[b]Common trap:[b] Students often assume that more statements must lead to sufficiency, or they try to manipulate the inequalities without recognizing what question they're actually answering. In this problem, no amount of information about Mario's total money helps unless we know the relative prices.
[b]Takeaway:[b] In "enough money" Data Sufficiency problems, always identify the underlying comparison being tested. Here, it was simply "which costs more, cookies or drinks?" Once you see that, testing becomes much faster.[/b][/b][/b][/b][/b][/b][/b][/b][/b][/b][/b][/b][/b][/b][/b][/b][/b][/b][/b][/b][/b][/b][/b]
Let M = Mario's total money
What we know:[b] M ≥ 4d + 2c (he can afford 4 soft drinks and 2 cookies)
[b]What we need to know:[b] Is M ≥ 4c + 2d? (Can he afford 4 cookies and 2 soft drinks?)
Here's the key insight: We're really asking whether 4c + 2d ≤ 4d + 2c
Simplifying: 2c ≤ 2d, or [b]c ≤ d[b]
So the entire question boils down to: Are cookies cheaper than or equal to soft drinks?
[b]Statement (1): Mario has enough money for 3 cookies and 3 soft drinks[b]
M ≥ 3c + 3d = 3(c + d)
We already know M ≥ 4d + 2c. Does this tell us whether c ≤ d?
Try c = $2, d = $3: Then 4d + 2c = $16, and 3c + 3d = $15. If M = $16, both conditions work. Is c ≤ d? Yes (2 ≤ 3), so he CAN afford 4c + 2d = $14.
Try c = $3, d = $2: Then 4d + 2c = $14, and 3c + 3d = $15. If M = $15, both conditions work. Is c ≤ d? No (3 > 2), so 4c + 2d = $16, which exceeds his money.
[b]NOT SUFFICIENT[b]
[b]Statement (2): Mario has enough money for 6 cookies[b]
M ≥ 6c
This tells us nothing about d. We can't compare c and d.
[b]NOT SUFFICIENT[b]
[b]Combined (1) + (2):[b]
From (1): M ≥ 3c + 3d
From (2): M ≥ 6c
Given: M ≥ 4d + 2c
Using the same number tests from Statement (1), even with both statements we still can't determine whether c ≤ d. The statements give us bounds on M, but not the price relationship we need.
[b]STILL NOT SUFFICIENT[b]
[b]Answer: E[b]
[b]Common trap:[b] Students often assume that more statements must lead to sufficiency, or they try to manipulate the inequalities without recognizing what question they're actually answering. In this problem, no amount of information about Mario's total money helps unless we know the relative prices.
[b]Takeaway:[b] In "enough money" Data Sufficiency problems, always identify the underlying comparison being tested. Here, it was simply "which costs more, cookies or drinks?" Once you see that, testing becomes much faster.[/b][/b][/b][/b][/b][/b][/b][/b][/b][/b][/b][/b][/b][/b][/b][/b][/b][/b][/b][/b][/b][/b][/b]
14 Feb 2026, 06:28
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So the entire question boils down to: Are cookies cheaper than or equal to soft drinks?
This is not true
This is not true
