Dinner Age

Logic Level 2

A professor tells her assistant that she dined with three people the previous night. She also tells him that the sum of the three people's ages is twice the secretary's own age and that the product of the three people's ages is 2450. Then, she asks him to tell her the ages of the three people. After a while, the assistant tells the professor that he doesn't have enough information to solve the problem. She agrees and adds that she is older than all three people with whom she dined. The assistant, who knows her age, promptly gives the professor the correct ages.

What are the ages of all five people in this story?

CREDIT GOES TO CALPOLY.EDU AND MARYLIN VOS SAVANT'S COLUMN "Ask Marilyn"

Secretary 32; Professor 50; Guests 49, 10, 5 Secretary 31; Professor 55; Guests 49, 10, 5 Secretary 33; Professor 62; Guests 43, 15, 3 Secretary 53; Professor 61; Guests 10, 50, 7

Jenny Wen by Jenny Wen , 22, USA

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3 solutions

Sayantan Mondal
Mar 16, 2018

Just options checking

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Mohammad Khaza
May 19, 2018

it could have been a good problem if the options were removed and a extra data was involved to solve this.

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Jenny Wen
Mar 14, 2018

Consider all factorizations of 2450 into integers a, b, c. (Since these three variables represent ages, all factors above 98 should be excluded!) The remaining triples (a,b,c) sum to distinct values except 50+7+7 = 49+10+5 = 64. Since the assistant did not have enough information at this point, one of these two triples must be the correct answer; in particular, the secretary's age is 64/2 = 32. If the professor is 49 years old or younger, her assertion about being older than all others at dinner cannot be true; if she is 51 or older, that information would not help the assistant. Hence, the professor is 50, and her dinner guests had ages 49, 10, 5.

Note that the question and the answer are copied exactly from calpoly.edu

0 Helpful 0 Interesting 0 Brilliant 0 Confused

But why don't you just RANDOM GUESS?????????????????????????????????????????????????????????????????????????????????

caillen tu - 1 year ago

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