<p>1) In 1995, Diana read 10 English books and 7 French books. In 1996, she read twice as many French books as English books. If 60% of the books that she read during the 2 years were French, how many English and French books did she read in 1996?
(A) 16
(B) 26
(C) 32
(D) 39
(E) 48 --> Answer</p>
<p>The books say's : 3/5 = 7+2x/17+3x
My question is why 7+2x(which is french over total)? Why not let's say 10+x(english over total) ?</p>
<p>French over total ->
7+2x / 7+2x+10+x = 7+2x / 17+3x</p>
<p>Remember, French over total, NOT French over English.</p>
<p>I understand that. My question is, why is it french over total? Why not english over total?</p>
<p>because 60% is french of the total 100% all books.
(7+2x)/(17+3x) = .6
7+2X = 0.6(17+3X)
7+2X = 10.2 +1.8X
2x-1.8X= 10.2-7
.2x = 3.2
x = 16
oops the total books = 3x= 48</p>
<p>Take a simple example to understand.
You have 5 Black books, and 5 Blue books. What is the percentage of Black books?</p>
<p>Is it Black / Blue aka 5/5? No, because that’s 1. It’s Black over total which is 1/2 which is 50%.</p>
<p>There are very basic math concepts, you should know these already. Fraction of anything or percentage of anything is always “Portion over Total”.</p>
<p>You should start trying to employ cheap tricks for the SAT, they can help a lot. I didn’t know how to do this one so I simple went through all the answer choices, adding the number in the answer with 17 (books she read in 95) and then multiplying by .6 (Amount of French books she read). You should know that only one answer, when multiplied by .6, will give you a whole number, rather than a decimal. </p>
<p>You should try to learn all the math concepts, but also learn some of these tricks, they can be very beneficial.</p>
<p>^^</p>
<p>Good tip, SAT100. Fwiw, those are not cheap tricks; such methods are poweful reasoning methods, and that is what the SAT is all about. </p>
<p>In this case, you could also look at a simpler test. </p>
<p>The clue “In 1996, she read twice as many French books as English books” means that the answer has to be divisible by THREE. Only 39 and 48 work.</p>
<p>From there, it’s fast to check by adding 13/26 or 16/32 to 10/7.</p>