Hello,

#10: A second grade class is writing reports on birds. The students' teacher has given them a list of 6 birds they can choose to write about. If Lizzie wants to write a report that includes two or three of the birds, how many different reports can she write?

Solution: First find the number of 2-bird reports - YYNNNN, then consider the number of 3-bird reports - YYYNNN, add them together.

HOWEVER, isn't it the case that if you pick one bird, you will have to pick another one? i.e. you wouldn't write 2 reports on the same bird?

Also:
#13: Mario's Pizza has 2 choices of crist: deep dish and thin-and crispy. The restaurant also has a choice of 5 toppings: tomatoes, sausage, peppers, onions and pepperoni. Finally, Mario's offers every pizza in extra-cheese as well as regular. If Linda's volleyball team decides to order a pizza with four toppins, how many different choices do the teammates have at Mario's Pizza?

Solution: Consider the toppings first: YYYYN

HOWEVER, if they picked one topping, wouldn't they not pick it again?

Finally:
#7: A British spy is trying to escape from his prison cell. The lock requires him to enter one number, from 1-9, and then push a pair of colored button simultaneously. He can make one attempt every 3 seconds. If there are 6 colored buttons, what is the longest possible time it could take the spy to escape from the prison cell?

Solution: The different pairs of colored buttons - YYNNNN

HOWEVER, if he had to press the colored buttons simultaneously, then if he pressed one color button, couldn't he not press it again?

Thank you.

Yes to all three. The anagram grid method already factors this in. For example, the grid YYNNNN already says that you pick 2 (different) birds and do not pick the other four birds. The six letters represent the 6 different birds. And so on for the other examples.

_________________
Stacey Koprince
Instructor
Director of Online Community
ManhattanGMAT

@Stacey

Regarding question #7 "A British Spy..." - The official answer in the book is 135 combinations x 3 seconds per attempt = 405 seconds.

BUT wouldn't the spy make his first attempt at 0 seconds on the stopwatch? So he would have only 135 - 1 = 134 three second intervals. Making the answer 134 x 3 = 402 seconds??

riakhiani,
That's actually a very interesting point. I think you have to assume that it takes some period of time to actually push the buttons, hence 145 tries, each taking three seconds. If you read the explanation on page 79, it says "each try takes 3 seconds". However, I can see your point that we should assume that a try can be registered at time zero seconds exactly.

I doubt that the GMAT would try to trip you up by this kind of hair splitting, but this is a good observation. Maybe another instructor will chime in as to what he/she thinks is going on here.

Thank you,

_________________
Jamie Nelson
ManhattanGMAT Instructor

@jnelson0612,

Thanks for your reply.

I actually did notice the difference in wording between the question and the explanation - The question says "He can make one attempt every 3 seconds", which seems to imply that the buttons won't register more than 1 try in any 3 second period and so the spy has to wait for 3 seconds after each try. I think it would be a little unfair to assume that 135 tries is like a distance that he has to cover and his rate is 1 attempt per 3 seconds.

I do agree that the GMAT would never test us on such word play. In fact, the GMAT is extremely meticulous in the language it uses in framing its questions - ensuring that the wording is clear and never open to more than 1 type of interpretation!

The reason I brought this up is because I think that either the question or its explanation require some modification in future editions.

riakhiani, I agree. I'll pass on your comments for a further edition. Thank you!

_________________
Jamie Nelson
ManhattanGMAT Instructor

In the Mario pizza ... question nowhere is it mentioned that all four topping have to be different. If that is the case then the answer 5*2*2= 20 is incorrect if we can have the same topping twice , 3times etc. Wouldn't the answer be 70*2*2 = 280?

Do i make this assumption during the test unless specified no repetitions ?

thanks
Zen

Yes, on the real test, they'd say you could only pick a topping once. :)

_________________
Stacey Koprince
Instructor
Director of Online Community
ManhattanGMAT

P.76 #13 Word Translations

@Stacey/GMAT Instructors

I want to follow up on Zen's question. He/she indicated that if we can choose the toppings more than once (repetition), I can't seem to figure how he/she calculated 70. I assume the answer would be 625 rather than 70.


5 choices (4 toppings) would equal 625.

625 = 5 choices * 5choices * 5choices * 5 choices

625 * 2 * 2 = 2500

Please correct me if I am wrong. Thanks.

this is wrong, because your number includes both of the following topping selections, which are functionally identical:

tomato
tomato
peppers
onions

peppers
tomato
onions
tomato

accounting for this overcounting is WAY beyond the difficulty i've seen on the hardest GMAT problems i've ever encountered, so it's not worth getting into the exact method of calculation here. as for the number 70, believe it or not that is the correct number! now i'm interested in how Zen got that number using standard GMAT techniques..

_________________
Tim Sanders
Manhattan GMAT Instructor