Brian is selling souvenirs outside of a Detroit Tigers baseball game.

Question

Brian is selling souvenirs outside of a Detroit Tigers baseball game. He is selling two different items: T-shirts (T) are selling for $22 each and Baseball caps (C) are selling for $19 each. How many T-shirts did Brian sell?

(1) Brian sold a total of 8 souvenirs.

(2) The total value of the souvenirs that Brian sold was $161.

shriramvelamuri · Answer

I think the asnwer is B.

Stem: T =22; C= 19.

St: T+C= 8.

Any combination possible.

St2 : 22T+ 19C= 161.

The only combinatin possible is T= 3 and C=5.

Hence option B.

longfellow · Answer

The answer seems to be B

22t+19c=161
t=3
c=5

peachfuzz · Answer

Brian is selling souvenirs outside of a Detroit Tigers baseball game. He is selling two different items: T-shirts (T) are selling for $22 each and Baseball caps (C) are selling for $19 each. How many T-shirts did Brian sell?

(1) Brian sold a total of 8 souvenirs.
Insufficient, no break down

(2) The total value of the souvenirs that Brian sold was $161.
22×#ofshirts+19×#ofcaps=161
Turns out shirts = 3 and caps = 5
Sufficient

Answer: B

goldfinchmonster · Answer

Can anyone tell how to figure out that 161 can be also written as 22*3 + 19*5. ..? Is hit and trial the only method... :!:

Actually when ever i encounter such situation where a bigger number is to be re-written in the form of small numbers, i go for prime factorisation and in this case i did the same and the values were 7 & 23 ( of no use ). Is there any flaw in my approach. Hope someone clarifies my doubt, and thanks in advance... :-D

kunal555 · Answer

Statement 1:- 
Doesn't provide any information about the T-shirts sold.
INSUFFICIENT

Statement 2:-
Let T be the number of t-shirts and C be the number of caps.
then 
22T + 19C = 161
or 22 T = 161 - 19C

or  T= \frac{161-19C}{22}

Now start plugging in values of C starting with 0 to check if we get integer values for T.
At C=5, we get T=3.
This is the only possible integral value of T we can get from the above equation.
SUFFICIENT

Answer:- B

Bunuel · Answer

VERITAS PREP TUTOR OFFICIAL SOLUTION:

This question points convincingly toward answer choice C. If you convert the two statements to equations you get T + C = 8 and 22 T + 19 C = $161. With these two equations together it is possible to solve for the answer.

Yet before you choose C, take a closer look at statement 2 . This is not an ordinary equation with negligible coefficients for the variables. This equation has coefficients of 22 and 19! These are unusual numbers and they are not easily interchangeable the way that smaller coefficients would be. Additionally, the total value of souvenirs sold is just $161, meaning that there is not much room to trade t-shirts for caps. When you combine this fact with the large coefficients this means that there will be very few options for the values of T and C. And remember – you can’t buy 1/4 of a cap (even if your hat size is 71/4), so T and C must be integers. The “backdrop” of this problem adds substance to the shape of these puzzle pieces.

In order to determine if statement 1 is needed or if statement 2 is sufficient on its own, you could check to see whether or not statement 2 allows for different total numbers of souvenirs. For example, could Brian have sold fewer than 8 souvenirs? (The reason we start with 8 souvenirs is because we took a peek at statement 1. We are not relying on statement 1, we are just getting an idea that 8 souvenirs would be an acceptable total and we are looking for other acceptable totals).

So, what about 7 souvenirs? Could that total work? Actually, no. Even if we choose 7 of the more expensive souvenirs, the t-shirts, we find that 7*22 = $154. This is not enough money. We need the total value to be $161. So, we cannot have fewer than 8 total souvenirs. (The reason we cannot have ,say, 7.5 total souvenirs is that there is a hidden fact here and that is that you cannot have a portion of a T-shirt or a fraction of a cap. In other words we know that we must have integer values for T and C and for the total number of souvenirs as well).

What about having more than 8 souvenirs? If we try having 9 of the cheaper souvenirs we find that 9*19 = $171. That is too much money. Therefore we know that it is impossible to have more than 8 souvenirs, we must have exactly eight t-shirts and caps combined.

Statement 2 – the puzzle equation –provides us with a second hidden equation T + C = 8 . This is the only information that statement 1 offers, therefore, we do not need statement 1. Statement 2 alone gives us both equations. And the correct answer is B.

If this were a problem solving question you could now use the two equations T + C = 8 and 22 T + 19 C = 161 to solve for the number of T-shirts that Brian sold. Since this is Data Sufficiency we do not need to solve it, however, we just need to get to the point where we are certain that we can solve it.

Before you choose answer choice C on a problem like this be sure to check for a puzzle equation – one that only fits together in just a single way. You might get two equations for the price of one. And remember this – Data Sufficiency problems are more often logic puzzles featuring numbers than they are just “math problems”. So the jigsaw analogy works – when you’re solving puzzles, pay particular attention to the way the pieces are put together!

atshy21saraf · Answer

*********
In general, when you have two variables and one equation you will not have enough data to solve. There is at least one important exception:

✔ If your equation is of the form Ax + By = C where A, B and C are known, and
✔ if your unknowns are positive integers, and
✔ if C < the least common multiple of A & B, then
the equation has only 1 solution!
*********

Bunuel Is this true??

This concept is presented in one other problem by nrl.amin here: in-the-first-hour-of-a-bake-sale-students-sold-either-cho-154036.html#p1767346

bazu · Answer

Is this a rule of thumb? have you checked it in different problems? (just want to see how reliable it is in case of time constraints)

siddhantvarma · Answer

Bunuel   KarishmaB 
How to figure out the values for the amount of T-shirt and Cap from the equation 22T + 19C = 161 time-efficiently? I start plugging in all possible values and it takes a long time for me to reach the answer. Is there a trick to quickly getting to the right numbers? I've seen such questions multiple times, and while it does occur to me that maybe just knowing the equation is enough even with two variables since there's a possibility of getting a unique pair of integers that satisfies this equation, however using hit and trial to get to that pair takes a lot of time. It also feels like a shot in the dark and using this approach when a timer is on your head I also often end up messing up the calculations.

KarishmaB · Answer

Use logic. There is bound to be some.

22T + 19C = 161

I see that the first term will be even. So I will try only odd values for C. Also, divisibility by 11 is simple to check so it makes sense.

Put C = 1, I get 22T = 142 (142 is not divisible by 11 so ignore)
Put C = 3, I get 22T = 104 (104 is not divisible by 11 so ignore)
Put C = 5, I get 22T = 66 
So T = 3 and C = 5

It helps if you know the multiplication table of 19.

KarishmaB · Answer

It is a DS question. Think: Do we really need to solve it? Using statement 2: 22T + 19C = 161 We know there is bound to be a value for T and C since this is a real life situation. The total was $161. The total number of Ts and Cs together will be about 8 because their average is about 20. So we might get soemthing like T = 2, C = 6 or T = 3, C = 5 etc. Once we will get it, will we find another set of values? Absolutely not! Check here why: https://anaprep.com/algebra-integer-sol ... variables/

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Brian is selling souvenirs outside of a Detroit Tigers baseball game.

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Brian is selling souvenirs outside of a Detroit Tigers baseball game.

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