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HURDLE-01 : NUMBERS

(Solve this Hurdle by 22nd Jan.)

Natural Numbers consists of the common numbers like 1,2 ,3 ...etc.  The number Zero is not included.    N = {1, 2, 3, 4, … }

Whole Numbers consists of the set of Natural Numbers and the number 0.

Prime Number is a natural number greater than which has only 1 and itself as factors.

Composite Number  is a natural number greater than 1 that has more factors than 1 and itself.

The natural number 1 is neither a prime number nor a composite number.

Integers  consists of the Whole Numbers and their negatives.  {…,-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 …}

Rational Numbers consists of all numbers that can be written as fractions.

Irrational Numbers  consists of numbers that cannot be written as fractions.

Rational Numbers together with the set of Irrational Numbers is called the set of Real Numbers.

Complex Numbers  consists of the set of numbers that can be written in the form a + bi where i = square root of -1.

Q1.  6 odd natural numbers that add up to a total of 33. Select the right option :
a) One of the number has to be 1.
b) One of the number has to be 3.
c) One of the number has to be  7.
d) One of the number has to be 5.
e) There is no solution for this.

Q2. a,b and c are 3 consecutive whole numbers. a^2 +b^2 +c ^2 = Z
Z will always be : a) Square number  b) Odd number  c) Even number  D) none of these .

Q3. a,b,c and d are four consecutive whole numbers. a^2 +b^2 + c^2 + d^2= Z
Z will always be : a) Square number  b) Odd number  c) Even number  D) none of these

Q4. a,b and c are three consecutive whole numbers. a^2 - b^2 + c ^2 = Z. ( UrPercentile.com)
Z will always be : a) Square number  b) Odd number  c) Even number  D) none of these .

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TO FIND OUT IF A NUMBER IS DIVISIBLE BY SEVEN:
Take the last digit, double it, and subtract it from the rest of the number.
If the answer is more than a 2 digit number perform the above again.
If the result is 0 or is divisible by 7 the original number is also divisible by 7.

Example 1 ) 259
9*2= 18.
25-18 = 7 which is divisible by 7 so 259 is also divisible by 7.

Example 2 ) 2793
3*2= 6
279-6= 273
now 3*2=6
27-6= 21 which is divisible by 7 so 2793 is also divisible by 7.

Now find out if following are divisible by 7

Q5. 2841
Q6. 3873
Q7. 1393
Q8. 2877

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TO FIND SQUARE OF A NUMBER BETWEEN 40 to 50

Sq (44) .
1) Subtract the number from 50 getting result A.
2) Square A getting result X.
3) Subtract A from 25 getting result Y
4) Answer is YX

EXAMPLE 1 : 44
50-44=6
Sq of 6 =36
25-6 = 19

EXAMPLE 2 : 47
50-47=3
Sq 0f 3 = 09
25-3= 22
So answer = 2209

Q 9. NOW TRY To Find Sq of 48 ,26 and 49

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TO FIND SQAURE OF ANY TWO DIGIT NUMBER

Square the last digit to get result A.
Multiply the two digits and double it to get result B.
Square the first Digit to get result C.
The final result will be as follows :
Last digit of the final result will be the last digit of A.
The second last digit of the final result will be B + any carryover
from A.  ( UrPercentile.com)
The third and fourth digit of the final result will be C + any
carryover from B .

EXAMPLE 1 : Sq(53)

A= 3*3 =9
B= 2*5*3=30
C= 25
Result =
Last Digit =9
Second Last digit = 0 (from B which is 30).
Third and fourth last digit will be C+ 3 carried over from B ( B is 30)= 25+3=28.

The Result = 2809

EXAMPLE 2 : Sq(71)
A= 1*1=1
B=2*7*1=14
C=49

Result =
last digit = A which is 1
Second last Digit = 4 from B which is 14.
Third and fourth last digit will be C+1 ( 1 carried over from B
which is 14) 49+1=50
The result 5041

Q10. Now Find out Square of 44, 48, 38, 97.

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TO FIND SQUARE OF A 3 DIGIT NUMBER :

LET THE NUMBER BE XYZ
SQ (XYZ) is calculated like this

STEP 1. Last digit = last digit of SQ(Z)
STEP 2. Second Last Digit = 2*Y*Z + any carryover from STEP 1.
STEP 3. Third Last Digit 2*X*Z+ Sq(Y) + any carryover from STEP 2.
STEP 4. Fourth last digit is 2*X*Y + any carryover from STEP 3.
STEP 5 . In the beginning of result will be Sq(X) + any carryover from Step 4.

EXAMPLE :

SQ (431)

STEP 1. Last digit = last digit of SQ(1) =1
STEP 2. Second Last Digit = 2*3*1 + any carryover from STEP 1.= 6
STEP 3. Third Last Digit 2*4*1+ Sq(3) + any carryover from STEP 2.= 2*4*1 +9= 17. so 7 and 1 carryover
STEP 4. Fourth last digit is 2*4*3 + any carryover (which is 1) . = 24+1=25. So 5 and carry over 2.
STEP 5 . In the beginning of result will be Sq(4) + any carryover from Step 4. So 16+2 =18.

So the result will be 185761.

If the option provided to you are such that the last two digits are different, then you need to carry out first two steps only, thus saving time. You may save up to 30 seconds on each calculations and if there are 4 such questions you save 2 minutes which may really affect UR Percentile score.

So if the answer of some question is SQ(527) and the options are

1) 278779
2) 277729
3) 279849
4) 277859

You just need to carry out the first two steps and you can select the correct answer.

STEP 1 LAST DIGIT= SQ(7) = 49 . So last digit =9 and 4 carryover.
STEP 2 : Second Last digit = 2*2*7 +4(Carryover)= 28+4 = 32 . So the second last digit is 2. Now you may select 2 as the correct answer as only it has 9 as the last digit and 2 as the second last digit.

Q11. Now Find Sq of following numbers : 323, 282, 461.

Would suggest you to memorize the some of the square, cube, decimal, percentages, tables . There is a file named "tables.xls" in our files section you can download for this. Try the link below :

http://groups.yahoo.com/group/urpercentile/files/DI%2C%20DS%2C%20Quants/tables.xls

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VOCABULARY :

1) Accursed : Evil, horrible
2) adventitious : accidental, casual, developing in an unusual position.
3) coalescence n. The act or process of merging to form one body, combination, or product.
4) deducible : derived by reasoning
5) jettison : throw overboard from ship , aircraft or vehicle. To  reject an idea.
6) leeward n. That side or direction of a ship that is away from the wind.
7) obstinacy n. Stubborn adherence to opinion, determined not to agree with others and unwilling to change.
8) Obdurate : Not easily persuaded . Impassive to feeling of humanity, Stubborn
9) Perfidious :: basely false, faithless, treacherous
10) Revulsion : sudden violent change of feeling; reaction
11) Poultice : A soothing application applied to sore and inflamed parts of the body to ease pain.
12) Vulnerable adj. Capable of receiving injuries or exposed to possible damage.
13) Rapprochement : renewal of friendly relations between people or nations that were previously hostile.
14) Recapitulate : To repeat again the main points, or steps.
15) Revulsion : sudden violent change of feeling; reaction

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