If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

# GMAT: Math 5

24-29, pgs. 155-156. Created by Sal Khan.

## Want to join the conversation?

• What are vertices?
• verticles are like the y and x axis on a graph
• how do i solve this problem (5th grade) which number below has a 3 that has a value 1/10 as much as the 3 in 9,532.07 a.8,447.36 b.7.143.14 c.3,748.51 d.5,307.06
• #29 a how did both 16's turn into one 16?
• #24 why x + 18? can someone please explain this one to me further. Thank you!
• Can anyone explain #29 better? If he factors out 32 as 16 * 16, then 8(16 * 16), then cancels out one of the 16s, why does he still have the initial 16 at the start of the equation (16 * 20)? That makes very little sense to me.
And how does he end up at 16(20 + 16)? Where did the unaccounted for large number go that would have been the result of 8 * 32?
• The question is √(16∙20 + 8∙32), so I will explain what he is doing, then try to answer your questions:
So, you could just use PEMDAS and grind through all that math, OR you can factor out a common factor and use distribution to do the heavy lifting in just a few seconds. Remember that distribution is that handy math property so that
4(m + n) = 4m + 4n
but also, 4m + 4n can be factored to 4 (m + n)
It is a great time-saver in mental math, and also an important basis for algebra.
In his case, he is using 16

If I rewrite this original problem as
√(16∙a + b∙32), it is easier to see that both 16 and 32 contain a juicy factor equal to 16. You can use distribution to take out 16 from both those terms:
√(16∙a + b∙32) = √(16(a + 2b))
Now we make use of the fact that √XY = √X∙√Y and the first part here is √16
Let's see what is left when 16 is factored out of each term of the (16∙20 + 8∙32)

So, since
a = 20
b = 8
when we separate out the 16, we have (a + 2b)
that means we have 20 + 2∙8 which equals 20 + 16 = 36
So √16 ∙ √36 is the result, which we can recognize as 4 ∙ 6 = 24, the answer

I actually was more ambitious than Sal. I saw that √(16∙20 + 8∙32) can be rewritten as
√(`16∙4`∙5 + `8∙8`∙4) =√(64∙5 + 64∙4) = √64(5 + 4) =√64 ∙ √(5 + 4) = √64 ∙ √9 = 8∙3 = 24

The grinding way is √(16∙20 + 8∙32) = √(320 + 256) = √576
Not a lot of people recognize that square root without a calculator, but it is the exact same answer of 24 (That is √576 = 24)

Now, what he says about the 32 is that 32 = 16 times 2, and he wrote 16∙2 not 16²
In that row, he had 8∙16∙2 which equals 16∙16, which he wrote as his next row. There is NO extra 8 times 16∙16
He probably should have spaced the numbers better.
• in question 24 , i cant understand why is the answer not 22 .. cant get it
(1 vote)
• The total length of the rope according to the question stem is 40 feet. Also given, is that the rope can be cut into two segments, one of which is 18 feet longer than the other so the two segments can be represented as x (shorter segment) and x+18 (longer segment). From there, you can set up the equation: shorter segment + longer segment = 40. Alternatively, another way of writing this is x + x+18 = 40 or 2x +18 = 40. Solving for x, you get 2x = 22 (after subtracting 18 from both sides) which simplifies to x = 11 feet. Hope this helps.
• how do you divide fractions
(1 vote)
• if X/Y is a fraction and A/B is another fraction .
Then (X/Y)/(A/B) = (X x B)/(Y x A) .
For Example , (2/3)/(4/5) = (2 x 5)/(3 x 4) = 10/12 .
You can further simplify them by dividing the numerator and denominator by common factors.
In case of 10 and 12 , 2 is a common factor . so you divide 10 by 2 , you get 5 , similarly , you divide 12 by 2 , you get 6 . so 10/12 = 5/6 .
(1 vote)
• A board measureing 30 5/6 is to be cut into 3 equal places. How long will each piece be?
Express the answer using the same format as the orinal board length as a whole number and
Fraction. Additionally express the answer as a number rounded to two decimal points.
(1 vote)
• suppose you can send 2 text messages per minute, how many text messages you can send in 25 days
(1 vote)
• lets convert this into a mathematics equation.
The texting rate is 2 text/ minute.
60 minutes/ 1 hour is equivalent in time.
24 hours/ 1 day is equivalent in time.
The number of days is 25 so we will leave it as 1/25 days
now to multiple
(2 texts/ 1 minute)*(60 minutes/ 1 hour)*(24 hours/ 1 day)*(1 day/25 days)
Everything crosses out aside from 72,000 texts/ 25 days. This means in 25 days you could text 72,000 times.
(1 vote)
• how do you find what x means in this video?
(1 vote)