There are three times as many hot dogs as pizzas and five times as

Question

There are three times as many hot dogs as pizzas and five times as many brownies as hot dogs in "Junk Food 'R' Us" restaurant. The restaurant sells only whole products (you cannot buy half a pizza, for example). How many brownies are there in the restaurant?

(1) There are at least 10 pizzas in the restaurant

(2) There are 32 hot dogs at most in the restaurant

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Edskore · Answer

This is a nice, clean example of the DS trap where each statement alone gives you a range, and only together do they pin down one number.

1. Set up the relationships. Pizzas = p, hot dogs = 3p, brownies = 5 times hot dogs = 15p. Since the restaurant only sells whole items, p has to be a positive integer. The question is really just asking for the value of p, since brownies = 15p.

2. Statement (1) says p is at least 10. That's not one number, it's an entire range, 10, 11, 12, and on. Brownies could be 150, 165, 180, anything. Not sufficient.

3. Statement (2) says hot dogs are at most 32, so 3p ≤ 32, meaning p ≤ 10.67, and since p is an integer, p ≤ 10. Again a range, p could be 1 through 10. Not sufficient alone.

4. Now put them together. p ≥ 10 and p ≤ 10 at the same time only leaves one value, p = 10. Brownies = 150. That's sufficient.

5. Answer is C.

The trap is that statement (2) feels like it's doing a lot of work because "at most 32" sounds precise, but an upper bound on a range from 1 to 10 is still a wide range on its own. I catch myself doing this, seeing a strong sounding constraint and assuming it's enough without checking how many values still fit. Whenever a DS question gives you "at least" in one statement and "at most" in the other on the same variable, that's usually your cue they're building toward C, so check the overlap before you commit.

odionam · Answer

H=3P, B=5H=15P
H: P: B = 3:1:15
St 1 P>= 10 so we can't conclude single answer From St 2 = H<=32 so no of possibility for H to so can't conclude by combing if P= 10 H=30 if P=11 H=33 which is not in range so by combining we get definite answer

TheAdmissionHub · Answer

Pizza (P), hot dog (H), brownies (B).

We know that:
 H=3P 
 B=5H=15P

Statement 1  
We know that  P≥10  which is not helpful, because we don't have a specific number, but a range of numbers.
 Not sufficient

Statement 2  
There are at most 32H, so:  P ≤\frac{32}{3} .
Since we know that P has to be integer,  P ≤ 10 .
The information gives again a range of numbers.
 Not sufficient

Statement 1 + Statement 2   
From st. (1):  P≥10 
From st. (2):  P ≤ 10 
The only possible value for P is 10, so the only possible value for brownies is 150.
 Sufficient

Answer: C

There are three times as many hot dogs as pizzas and five times as

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There are three times as many hot dogs as pizzas and five times as