GRE Quantitative Puzzles

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  • FACE VALUE VERSUS PLACE VALUE OR LOCAL VALUE OF NUMBERS OR DIGITS:

THE FACE VALUE OF A NUMERAL OR DIGIT IS ITS VALUE IRRESPECTIVE WHICH POSITION IT IS SITTING AT, IN A NUMBER, HOWEVER BIG OR SMALL. FOR EXAMPLE: IN 6666, THERE ARE 4 6’S, ALL WITH A FACE VALUE OF 6, BUT ALL 4 6’S HAVE DIFFERENT PLACE VALUES WHICH ARE 6000, 600, 60, AND 6

  • CO-PRIMES, OR RELATIVE PRIMES: 2 NUMBERS ARE CO-PRIME OR RELATIVELY PRIME IF THEIR HIGHEST COMMON FACTOR IS 1. EXAMPLES OF RELATIVE PRIME PAIRS ARE (49, 64), (81, 25), ETC.
  • FACTORIAL OF A NUMBER: THE FACTORIAL OF A NUMBER N IS THE CONTINUED PRODUCT OF ALL THE NUMBERS STARTING 1 THROUGH N. EXAMPLE: 8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 GENERALIZING, N! = N * (N-1) * (N-2) * (N-3) * …… * 3 * 2 * 10! IS ALWAYS EQUAL TO 1
  • HIGHEST COMMON FACTOR (HCF): THE HIGHEST COMMON FACTOR OF 2 NUMBERS IS THE PRODUCT OF ALL PRIME FACTORS (CONSIDERED HOW MANY EVER TIMES THEY MAY APPEAR IN DISINTEGRATING THE NUMBER INTO ITS PRIME FACTORS). EXAMPLE: THE HCF OF 144 AND 100 IS 2 * 2 = 4 (NOTICE THE 2 CONSIDER TWICE, BECAUSE THAT IS HOW MANY TIMES IT APPEARS WHEN EACH OF THE AFOREMENTIONED NUMBERS IS FACTORIZED INTO PRIMES)
  • LOWEST COMMON MULTIPLE (LCM): THE LOWEST COMMON MULTIPLE OF 2 NUMBERS IS THE PRODUCT OF THE HCF OF THE 2 NUMBERS WITH WHATEVER IS LEFT OVER AFTER DIVIDING EACH OF THE 2 NUMBERS BY THEIR HCF. RESULTANTLY, THE LCM = HCF * N1/HCF * N2/HCF IF WE CHANGE OUR ANGLE OF VIEW BY A BIT, WE NOTICE THAT LCMN1,N2 = N1 * N2 / HCF
  • HCF & LCM PRODUCT:                                                                                                        THE HCF IS ALSO CALLED THE GREATEST COMMON DIVISOR (GCD).                        THE PRODUCT OF 2 NUMBERS N1 AND N2 IS EQUAL TO THE PRODUCT OF THEIR HCF AND LCM, THAT IS, N1 * N2 = HCF * LCM
  • HCF AND LCM OF FRACTIONS:                                                                                    HCF OF FRACTIONS = HCF OF NUMERATORS / LCM OF DENOMINATORS                LCM OF FRACTIONS = LCM OF NUMERATORS / HCF OF DENOMINATORS
  • BODMAS RULE:                                                                                                       BODMAS STANDS FOR BRACKET, OF, DIVISION, MULTIPLICATION, ADDITION, SUBTRACTION. THUS, WHILE SIMPLIFYING ANY EXPRESSION, THE BRACKETS, MUST BE REMOVED FIRST, STRICTLY IN THIS ORDER : ( ),{ },[ ]. UPON REMOVAL OF BRACKETS, WE MUST COMPLETE THE OTHER OPERATIONS IN THIS ORDER : OF , DIVISION , MULTIPLICATION , ADDITION , SUBTRACTION
  • SOME IMPORTANT FORMULAE:
  1. (A+B)^2 = A^2+2*A*B+B^2
  2. (A-B)^2 = A^2-2*A*B+B^2
  3. (A^2-B^2) = (A+B)(A-B)
  4. (A+B)^3 = A^3+B^3+3*A*B(A+B)
  5. (A-B)^3 = A^3-B^3-3*A*B(A-B)
  6. (A+B)^2+(A-B)^2 = 2*(A^2+B^2)
  7. (A+B)^2-(A-B)^2 = 4*A*B
  8. (A^3+B^3) = (A+B)*(A^2-A*B+B^2)
  9. (A^3-B^3) = (A-B)*(A^2+A*B+B^2)
  10. (A+B+C)^2 = A^2+B^2+C^2+2*(A*B+B*C+C*A) 
  • INDICES AND EXPONENTS:
  1. A^M * A^N = A^(M+N)
  2. A^M/A^N = A^(M-N)
  3. (A^M)^N = A^(M*N)
  4. (A*B)^M = A^M * B^M
  5. (A/B)^M = A^M / B^M
  6. A^0 = 1
  7. A^(-M) = 1/A^M
  8. THE NTH ROOT OF A = A^(1/N)
  9. THE NTH ROOT OF A*B = NTH ROOT OF A * NTH ROOT OF B
  10. THE NTH ROOT OF (A/B) = NTH ROOT OF A / NTH ROOT OF B
  11. THE MTH ROOT OF THE NTH ROOT OF A = THE (M*N)TH ROOT OF A

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