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11 Dec 2020, 07:47
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No Topping: 1
All Three Toppings: 3
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:
59% (01:52) correct
41%
(02:43)
wrong
based on 770
sessions
History
Date
Time
Result
Not Attempted Yet
Four friends, Anna, Boris, Clara, and Daniel, each ordered a vanilla ice cream cone. The vendor offered them the option to add sprinkles, chocolate sauce, or a cherry on top. Three friends chose sprinkles, three chose chocolate sauce, and three chose a cherry. The friend who skipped the sprinkles also skipped chocolate sauce, and the friend who skipped chocolate sauce also skipped the cherry.
Select for No Topping the number of friends who skipped all three toppings, and select for All Three Toppings the number of friends who chose all three toppings. Make only two selections, one in each column.
Select for No Topping the number of friends who skipped all three toppings, and select for All Three Toppings the number of friends who chose all three toppings. Make only two selections, one in each column.
| No Topping | All Three Toppings | |
| 0 | ||
| 1 | ||
| 2 | ||
| 3 | ||
| 4 |
ShowHide Answer
Official Answer
No Topping: 1
All Three Toppings: 3
23 Nov 2024, 06:39
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Bunuel
Official Solution:
Say Anna skipped sprinkles and chocolate sauce. If a different friend skipped chocolate sauce and cherry, then two friends would have skipped chocolate sauce, leaving only the remaining two to have added it. However, we know that three friends chose chocolate sauce. Therefore, the same person must have skipped all three toppings. As a result, the remaining three friends each added all three toppings.
Correct answer:
No Topping "1"
All Three Toppings "3"
Attachment:
GMAT-Club-Forum-b8pun68z.png [ 11.08 KiB | Viewed 1888 times ]
06 Dec 2024, 16:13
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1. Let's visualize the problem using a table:
2. "Three friends chose sprinkles, three chose chocolate sauce, and three chose a cherry."
3. "The friend who skipped the sprinkles also skipped chocolate sauce." Without loss of generality, let Anna skip those two toppings.
4. This means that since the sum for sprinkles and chocolate sauce is 3, then the other friends all got it.
5. "The friend who skipped chocolate sauce also skipped the cherry." First of all, only one friend could skip the cherry on top, since the sum is 3, and only Anna skipped chocolate sauce. So, Anna skipped the cherry on top too.
6. Our answer will be: No topping - 1 and All three toppings - 3.
| Anna | Boris | Clara | Daniel | Sum | |
| Sprinkles | ? | ? | ? | ? | ? |
| Chocolate sauce | ? | ? | ? | ? | ? |
| Cherry on top | ? | ? | ? | ? | ? |
2. "Three friends chose sprinkles, three chose chocolate sauce, and three chose a cherry."
| Anna | Boris | Clara | Daniel | Sum | |
| Sprinkles | ? | ? | ? | ? | 3 |
| Chocolate sauce | ? | ? | ? | ? | 3 |
| Cherry on top | ? | ? | ? | ? | 3 |
3. "The friend who skipped the sprinkles also skipped chocolate sauce." Without loss of generality, let Anna skip those two toppings.
| Anna | Boris | Clara | Daniel | Sum | |
| Sprinkles | ? | ? | ? | 3 | |
| Chocolate sauce | ? | ? | ? | 3 | |
| Cherry on top | ? | ? | ? | ? | 3 |
4. This means that since the sum for sprinkles and chocolate sauce is 3, then the other friends all got it.
| Anna | Boris | Clara | Daniel | Sum | |
| Sprinkles | 1 | 1 | 1 | 3 | |
| Chocolate sauce | 1 | 1 | 1 | 3 | |
| Cherry on top | ? | ? | ? | ? | 3 |
5. "The friend who skipped chocolate sauce also skipped the cherry." First of all, only one friend could skip the cherry on top, since the sum is 3, and only Anna skipped chocolate sauce. So, Anna skipped the cherry on top too.
| Anna | Boris | Clara | Daniel | Sum | |
| Sprinkles | 1 | 1 | 1 | 3 | |
| Chocolate sauce | 1 | 1 | 1 | 3 | |
| Cherry on top | 1 | 1 | 1 | 3 |
6. Our answer will be: No topping - 1 and All three toppings - 3.
