word problems - sentences into algebra

Question

Sentence : The sum of Richard's age and Cindy's age in years is 17 more than the amount by which Tim's age is greater than Kathy's age.

Translation : R + C = (T - K) + 17

I don't understand (T-K) part.
How 'Tim's age is greater than Kathy's age' can translate '(T-K)'.
Isn't it T > K ?

cxa0897 · Answer

Lets break it down, starting with the back half of the question:
"Tim's age is greater than Kathy's age."

So we know right away, T > K.

Next we can look at this part:
"is 17 more than the amount by which"
The "amount" is referring to the difference between T and K, which will be a positive number since Tim is older according to last part of the statement. That gives us T-K, (or |K-T| to cover all bases) which are the only options that produce a positive number

Once we know this, we can just plug in the 17+ and solve for the final equation

ccooley · Answer

If the text just said 'Tim's age is greater than Kathy's age,' you'd be correct. That would translate as T > K.

However, it actually reads 'the amount by which Tim's age is greater than Kathy's age.'

Here's a much simpler problem with the same phrase in it:

'Tim is 84 years old. Kathy is 72 years old. What is  the amount by which Tim's age is greater than Kathy's age ?'

You're being asked for a quantity: how  much  older Tim is. In real life, you'd calculate that by taking 84 - 72, or T - K. On the GMAT, you do the same.

akela · Answer

Here is a great thread that discusses word problems: https://gmatclub.com/forum/word-problem ... 87346.html

JaeTPU · Answer

"Tim's age is greater than Kathy's age" is modifying the noun amount. So the  amount  by which Tim's age is greater than Kathy's age = the difference between Tim and Kathy's age, which is T-K (since Tim's age is presumably greater).

If the statement just said Tim's age is greater than Kathy's age, then it is T>K

Bunuel · Answer

You might find the below useful:

15. Word Problems 
     Theory   
 Word Problems Made Easy  
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 Age Problems 
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AvinashHaran · Answer

Let Richard's age: R
 Cindy's age : C
 Tim's age : T
 Kathy's age : K
sum of Richard's age and Cindy's age = R + C
amount by which Tim's age is greater than Kathy's age = difference of their ages (Where T > K) = T - K
17 more than the amount by which Tim's age is greater than Kathy's age = (T - K) + 17
Hence R + C = (T - K) + 17

word problems - sentences into algebra

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