# AlPhA KaPpA DeLtA PhI

Ucsd rambunctious ramblings – Inspirations from the Asian-American Interest Sorority..

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Category: GMAT Prep

## The Really Tough GMAT Question Series – 2

Oct 26

Hey People. Here is the next list of 10 Really Tough Gmat Questions. I am focusing on quants for the next few sessions. I will take up English after that. As always, please ping me on the site or leave a comment to clarify any doubts.

1. There are exactly n families – F1, F2,…. Fn – staying in Mr. Chang’s neighborhood. The number of members in the family Fn is n + 1. Mr.Chang decided to invite at most one member from each family for his birthday party. If the total number of ways in which he can invite a total of one or more members from his neighbourhood, is 2519, find n.

2. A solution of alcohol and water contains 60% alcohol. What percent of the solution must be taken out and replaced with water, so that the resultant solution contains 40% alcohol?
3.  If f (x) = 3x + 7 and f(f(f(x))) = 37, then the value of x =
(Hint: – x is between -2 and 2)
4. In a college of 525 students, each student takes at least two items from among pizza, egg white, egg yolk and cereal for his breakfast. If 375 students take pizza, 375 students take egg white, 375 students take egg yolk and 375 students take cereal for their breakfast, the number of students who take all the four items is at most
5. H(a, b, c, d) = 2a + 3bc + 4c2d. If a, b, c and d increase by 80%, 50%, 20% and 25% respectively, what is the percentage increase in H(a, b, c, d)?
6. Pradeep and Manohar started from A and B, towards B and A, at 6:00 a.m. and 7:00 a.m. respectively. They meet each other at 9:00 a.m. and continue towards their respective destinations. Pradeep, reaching B turns back and catches up with Manohar, before Manohar reaches A, at 11:00 a.m. At what time will Manohar reach A?
7. For what positive integral value of n, is 28 + 211 + 2n a perfect square? (n is one among 12, 13, 20)
8. The cost of five apples, four bananas and three chocolates is Rs.50. If the cost of an apple, a banana and a chocolate is Rs.12, how much more does an apple cost than a chocolate?
9. There are five sections – A, B, C, D and E – in class X of a certain school. In a certain test, the average mark of the students of sections A, B and C together is 60 and the average mark of the students of sections B, C and E together is also 60. If the ratio of the number of students in A and E is 1 : 2 and the average mark in the test of the students of sections A and E together is  find the average mark of the students of section A in the test.
1. n is 5
2. 33.33 %
3. -2
4. 225. (ping me for the solution..!!)
5. 80%
6. 6 PM.
7. 12
8. 2
9. 50

## The Really Tough GMAT Question Series – 1

Oct 24

Hi folks. Here are the first batch of 10 question in GMAT Quant. These questions have been prepared by me after working on the GMAT method of testing for almost a year now. Here goes.

1. In a queue, Monica is at the 14th position from the start and 18th position from the last. If Phoebe is at the middle of the queue, what is his position

2. In A years Richard will be B years old. How many years ago was he C years old.

3. Joe traveled at an average speed of 20 miles/hour when going from New York to Detroit. He traveled at an average speed of 30 miles/hour when coming back from Detroit to New York. Find his average speed.

4. Ross has 192 \$1 bills with him. It is his job to put each of them into a different bag. If Ross should be able to give out any amount between \$1 and \$192, what is the minimum number of bags that he should have.

5. Chandler and Joey run around Central Park (which happens to be a perfect circle of length 335 meters) in the same direction. Joey runs faster than Chandler. When they meet for the first time after starting, what is that extra distance that Joey would have covered over Chandler.

6. What is the area of the quadrilateral whose co-ordinates are (2,-2), (2,6), (15,2), (15,-4)

7. Chandler and Joey run around Central Park (which happens to be a perfect circle) in opposite directions. The ratios of their speeds are 1:3. Chandler, who knew about their speeds, says to Joey that they will meet at only 2 distinct points, even if they keep running till the next day. Joey laughs at Chandler and says that Chandler is wrong. Who is right, Joey or Chandler?

8. Rachael got 210 marks in an exam and ended up getting 300/11 percent more than the actual pass mark required. What is the minimum mark that Monica should aim at, in oder to at least clear the exam.

9. Ross leaves to meet Ben at exactly 4 PM. When he comes back, he notices that the hands of the clock are exactly 180 degrees apart. How long was Ross with Ben?

10. Joey likes to slice his pizza into into identical pieces before eating it. Just as he finishes slicing it, Chandler walks in and asks for 3/4ths of the pizza. Just as Chandler and Joey are about to eat their shares, Ross walks in and asks for  2/3 rds of Chandler’s share and 1/2 of Joey’s share. But Chandler gives Ross only 3/4 ths of what Ross asks and Joey gives what ever Ross asks. What is the share of the total pizza that Ross eats.

The Solutions:

1. 15

2. B – A – C

3. 24 miles/hour. Not 25 miles/hour..!!

4. 8  - (2^0,2^1, 2^2… 2^7 dollars in each bag.)

5. 335 meters.

6. 91 sq. units

7. Chandler is right. They meet at only 2 distinct points even if they keep running for ever. The first point is the start and the second point is 180 degrees opposite to the first one.

8. 165

9. 54 6/11 minutes

10. Ross eats one half of the pizza.

If anyone needs an explanation for any of the problems above. Drop in a comment. Will be happy to help. See you with the next batch of problems tomorrow.

## GMAT – Points to Remember

Apr 22

Miscellaneous Properties of Positive and Negative Numbers:

• The product (quotient) of positive numbers is positive.
• The product (quotient) of a positive number and a negative number is negative.
• The product (quotient) of an even number of negative numbers is positive.
• The product (quotient) of an odd number of negative numbers is negative.
• The sum of negative numbers is negative.
• A number raised to an even exponent is greater than or equal to zero.

Multiplication

• even × even = even
• odd × odd = odd
• even × odd = even
• even + even = even
• odd + odd = even
• even + odd = odd

Others

• Consecutive integers are written as x, x + 1, x + 2,
• Consecutive even or odd integers are written as x, x + 2, x + 4,
• The integer zero is neither positive nor negative, but it is even:
• Commutative property: x + y = y + x. Example: 5 + 4 = 4 + 5.
• Associative property: (x + y) + z = x + (y + z). Example: (1 + 2) + 3 = 1 + (2 + 3).
• Order of operations: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
• Squaring a fraction between 0 and 1 makes it smaller.
• When counting elements that are in overlapping sets, the total number will equal the number in one group plus the number in the other group minus the number common to both groups.
• The number of integers between two integers inclusive is one more than their difference.
• To solve a fractional equation, multiply both sides by the LCD (lowest common denominator) to clear fractions.
• You can cancel only over multiplication, not over addition or subtraction.
• Often you can solve a system of two equations in two unknowns by merely adding or subtracting the equations.
• A prime number is an integer that is divisible only by itself and 1.
• An even number is divisible by 2, and can be written as 2x.
• An odd number is not divisible by 2, and can be written as 2x + 1.
• Division by zero is undefined.
• Perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81 . . .
• Perfect cubes: 1, 8, 27, 64, 125 . . .
• If the last digit of an integer is 0, 2, 4, 6, or 8, then it is divisible by 2.
• An integer is divisible by 3 if the sum of its digits is divisible by 3.
• If the last digit of a integer is 0 or 5, then it is divisible by 5.

Common measurements:

• 1 foot = 12 inches
• 1 yard = 3 feet
• 1 mile = 5,280 feet
• 1 quart = 2 pints
• 1 gallon = 4 quarts
• 1 pound = 16 ounces
• 1 ton = 2,000 pounds
• 1 year = 365 days
• 1 year = 52 weeks

Elimination strategies:

•  On hard problems, if you are asked to find the least (or greatest) number, then eliminate the least (or greatest) answer-choice.
•  On hard problems, eliminate the answer-choice “not enough information.”
•  On hard problems, eliminate answer-choices that merely repeat numbers from the problem.
•  On hard problems, eliminate answer-choices that can be derived from elementary operations.
• After you have eliminated as many answer-choices as you can, choose from the more complicated or more unusual answer-choices remaining.

## Beat the Algebra Blues

Apr 20

As I sit down and prepare for the GMAT, I am starting to realize that the maths we learnt till K-12 was horribly below standard. Coming from the kind of schools I went to, rote learning was the norm. The schools pressurized the students to learn everything by-heart. The reason that we were given was that this approach would help out-score other students in the fiercely competitive SAT. That approach worked and worked well for me to secure a good college education. But the realization that my maths knowledge was poor came to me only from the last month.

The GMAT tests nothing more than basic algebra and its applications. Its is not the toughest exam in the world and certainly not the most demanding. Algebra 1 problems and Algebra 2 problems are simple but tricky. All it calls for is the recollection of basic algebra that we learnt in K-12. Algebra 1 covers linear equations, ratios and quadratic formulae; and Algebra 2 covers sequences-series, functions and factorization. Simple enough, you would say. But it wasn’t, for me at least.

If only I had some Algebra 1 help and Algebra 2 help available online, I would be a lot more confident now. If TutorVista’s services were known to me when I was in K-12 or at least in college, I would have made use of this. Algebra 1 answers and Algebra 2 answers would have been a lost easier for me at this stage.

Mathematics is a million dollar subject, they say. If that’s true, then algebra is worth most of that million. Wouldn’t hurt to enroll your kids in this service now, before it’s too late. TutorVista would give them the edge over their peers.