GMAT Math

Hi Papgust,

Is this correct or typo error?

6. If a/b = c/d, then a-b / b = c-d / b [Dividendo Rule]

right hand side should be c-d/d or c-d/b is only correct?

Regards,
Viju

viju9162 wrote:Hi Papgust,

Is this correct or typo error?

6. If a/b = c/d, then a-b / b = c-d / b [Dividendo Rule]

right hand side should be c-d/d or c-d/b is only correct?

Regards,
Viju

Thanks for pointing out . It's edited.

papgust wrote: Product of any 2 numbers = Product of LCM and HCF of those 2 numbers
Product of any 2 fractions = Product of LCM and HCF of those 2 fractions

How do I solve the following question:

A room is 2.47m long and 2.09m broad. It is required to pave the floor with minimum square slabs. Find the number of slabs required for floor.
(1) 142
(2) 143
(3) 165
(4) 225
(5) 361

papgust wrote:How to find REMAINDER for LARGE POWERS of numbers:


There are 2 ways to do so:

1. Pattern Method:

Example:

What is the remainder when 2^56 / 7 ?

Solution:
Remainder when 2^1 is divided by 7 is 2
Remainder when 2^2 is divided by 7 is 4
Remainder when 2^3 is divided by 7 is 1
Remainder when 2^4 is divided by 7 is 2 --> Repeats again.

The remainder repeats after 3 steps i.e. in the 4th step.

Now, Divide the power (or index) by 3 (no of steps after which remainder repeats) and compute a new remainder.

56 % 3 --> 2 (remainder)

Now, raise the base (2) to the power 2 (new remainder). 2^2 % 7 --> 4.

Thus, 4 is the remainder when 2^56 / 7.

.

im afraid i dont understand how u get a remainder of 2 when you divide 2 by 7 and a remainder of 4 when you divide 4 by 7, though you do get a remainder of 1 when you divide 8 by 7. could you please explain this..where am i going wrong?
2 divided by 7 will give me a remainder of 6, whereas 4 divided by 7 will give me a remainder of 5.

thanks, Preet

singhpreet1 wrote: im afraid i dont understand how u get a remainder of 2 when you divide 2 by 7 and a remainder of 4 when you divide 4 by 7, though you do get a remainder of 1 when you divide 8 by 7. could you please explain this..where am i going wrong?
2 divided by 7 will give me a remainder of 6, whereas 4 divided by 7 will give me a remainder of 5.

thanks, Preet

Hi Preet,

It isn't like that. when you divide 2 by 7, you only get a remainder of 2.

It's something like this -
1 / 5 --> remainder 1
2 / 5 --> 2
3 / 5 --> 3
4 / 5 --> 4
5 / 5 --> 0
6 / 5 --> 1
7 / 5 --> 2
and so on.

When you have a divisor of n (in this case 5), whatever dividend you may have, you will NEVER get a remainder of more than (n-1). Maximum remainder you could get is n-1. Remainder ranges from 0 to n-1

In this example, your remainder doesn't cross 4 when you divide any number by the divisor 5. In other words, your remainder ranges from 0 to 4 when you have a divisor of 5.

I suggest that you go through the basics of remainders. Pick any high school math book to understand the basics. If you don't have one, get hold of Manhattan GMAT 4th edition Number properties guide. It's really worth shelling out 26$ to understand the entire concepts of number properties.

@papgust ,

Thanks very much buddy for both the quants flash card and SC flashcards they are a great help . Its specially good to see u back here after your last GMAT attempt . Not only are you helping other, but I must say you are setting an example for people who are disappointed by their efforts and are on a verge of giving up .

Keep fighting buddy you will succeed one day .

Hope to see permutation and combination posts soon.

Well, thanks rockeyb once again! Sorry for a really long break. Got badly held up with work this week. Here we go!

--


SET THEORY:

For 3 set questions, there are 2 formulae that you can use.

Picture a Venn diagram; the first formula is just the sum of all of the various parts:
1. True # of objects = (# only A) + (# only B) + (# only C) + (# only AB) + (# only AC) + (# only BC) + (# only ABC)

The second formula is the one we use more often:
2. True # of objects = (total # A) + (total # B) + (total #C) - (# only AB) - (# only AC) - (# only BC) - 2(# ABC)

[Note that, technically, we should add a "+ (# with none of ABC)" to the end of each equation, but a 3 set question on the GMAT that had a "none" component is not often seen.]

We can simplify the second equation to:

True # of objects = (sum of total characteristics) - (sum of doubles) - 2(triples)

To understand why we have to subtract the doubles once and the triples twice, again picture a Venn diagram.

If an object is in the AB portion of the diagram, it's already been counted in the A circle and the B circle. In other words, it's been counted twice. To get a true count, therefore, we must subtract it once.

If an object is in the ABC portion of the diagram, it's already been counted in the A circle, the B circle AND the C circle. In other words, it's been counted three times. To get a true count, therefore, we must subtract it twice.

Here's the primary principle we're using:

Every object should be counted exactly once.



Courtesy: Stuart Kovinsky, GMAT Expert.

Examples:

In a consumer survey, 85% of those surveyed liked at least one of three products: 1, 2, and 3. 50% of those asked liked product 1, 30% liked product 2, and 20% liked product 3. If 5% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products?


Let's say there's 100 people, just to use numbers instead of percents. Since 85% like at least one of 3 products, we'll use 85 as our base number.

Since we have "at least one" information, we need to use the second formula:

True # of objects = (sum of total characteristics) - (sum of doubles) - 2(triples)

plugging in what we know:
85 = 50 + 30 + 20 - doubles - 2(5)
85 = 100 - 10 - doubles
85 = 90 - doubles
doubles = 5

The question is what % like more than 1, so we want to solve for:
doubles + triples
= 5 + 5 = 10

So, 10% is the final answer.

Examples: (Contd..)

There are 70 students in Math or English or German. Exactly 40 are in Math, 30 in German, 35 in English and 15 in all three courses. How many students are enrolled in exactly two of the courses? Math, English and German.

We use the exact same formula:
True # of objects = (sum of total characteristics) - (sum of doubles) - 2(triples)

70 = (40 + 30 + 35) - (doubles) - 2(15)
70 = 105 - doubles - 30
70 = 75 - doubles
doubles = 5

That's the end of "Set Theory". Really simple isn't it.. Knowing this stuff alone is more than sufficient for GMAT (trust me!)

I will be starting with "Co-ordinate Geometry" now.

POSITIVE/NEGATIVE slope: (A very important concept to know)


A line with a POSITIVE slope:

i. Passes through 1st and 3rd quadrant definitely.
ii. Passes through the 2nd quadrant (IF y-intercept is POSITIVE).
iii. Passes through the 4th quadrant (IF y-intercept is NEGATIVE).



A line with a NEGATIVE slope:

i. Passes through 2nd and 4th quadrant definitely.
ii. Passes through the 1st quadrant (IF y-intercept is POSITIVE).
iii. Passes through the 3rd quadrant (IF y-intercept is NEGATIVE).

Distance b/w 2 points:


Distance b/w points (x1,y1) and (x2,y2) = ROOT [(x1-x2)^2 + (y1-y2)^2]

Co-ordinates of point 'P' dividing the join of the two points (x1,y1) and (x2,y2) INTERNALLY in the ratio m:n is,

P(x,y) = [(m*x2 + n*x1) / m+n, (m*y2 + n*y1) / m+n]


Co-ordinates of point 'P' dividing the join of the two points (x1,y1) and (x2,y2) EXTERNALLY in the ratio m:n is,

P(x,y) = [(m*x2 - n*x1) / m-n, (m*y2 - n*y1) / m-n]


NOTE:
If ratio m:n has both m and n as POSITIVE, then its INTERNAL
If ratio m:n has one of m and n as NEGATIVE, then its EXTERNAL

Mid-point of a line:


Mid-point of a segment joining (x1,y1) and (x2,y2) is

(x1+x2 / 2, y1+y2 / 2)

Centroid (G) = (x1+x2+x3 / 3, y1+y2+y3 / 3)


NOTE: Centroid divides each median in the ratio 2:1.