## ã2.6.bã āĻ¸āĻŽāĻžāĻ¨ā§āĻ¤āĻ° āĻāĻŦāĻ āĻā§āĻŖā§āĻ¤ā§āĻ¤āĻ° āĻ§āĻžāĻ°āĻž āĻŦāĻŋāĻˇā§āĻ āĻĒā§āĻ°ā§āĻ¯āĻžāĻāĻāĻŋāĻ¸

[Math Center] 1. Quantity A Quantity B Â The sum of the odd integers fromÂ [latex]1[latex] to [latex]199[latex] The sum of the even integers fromÂ [latex]2[latex] to [latex]198[latex]   2. The sequence of numbersÂ [latex]{ a }_{ 1 },{ a }_{ 2 },{ a }_{ 3 }[latex]…Â [latex]{ a }_{ n }[latex].. is deīŦned by [latex]{ a }_{ n }=\frac{ […]

## ã2.5.bã āĻāĻ¸āĻŽāĻ¤āĻž āĻŦāĻŋāĻˇā§āĻ āĻĒā§āĻ°ā§āĻ¯āĻžāĻāĻāĻŋāĻ¸

[Math Center] 1.Â [latex]{ x }^{ 2 }y>0[latex] [latex]x{ y }^{ 2 }<0[latex] Quantity A Quantity B [latex]x[latex] [latex]y[latex]   2. On the number line shown above, the tick marks are equally spaced. Which of the following statements about the numbers [latex]x, y[latex], and [latex]z[latex] must be true? Indicate all such statements.  (A) [latex]xyz<0[latex] (B) […]

## ã2.5.a2ãāĻāĻ¸āĻŽāĻ¤āĻžāĻ° āĻāĻā§āĻ āĻĻā§āĻ°ā§āĻ¤ āĻāĻ°āĻ¤ā§ āĻāĻŦāĻŋ āĻāĻāĻā§āĻ¨

[āĻ¨ā§āĻāĻ āĻāĻ āĻāĻ°ā§āĻāĻŋāĻā§āĻ˛āĻāĻŋ (2) Algebra āĻŦāĻŋāĻ­āĻžāĻā§āĻ°Â āĻāĻ§ā§āĻ¨ā§Â ã5ãInequality āĻā§āĻ¯āĻžāĻĒā§āĻāĻžāĻ°ā§āĻ° āĻāĻ¨ā§āĻ¤āĻ°ā§āĻāĻ¤, āĻ¯āĻžÂ ã2.5.a2ãāĻāĻŋāĻšā§āĻ¨ āĻĻāĻŋā§ā§ āĻĒā§āĻ°āĻāĻžāĻļ āĻāĻ°āĻž āĻšā§ā§āĻā§] āĻāĻ¸āĻŽāĻ¤āĻžāĻ° āĻāĻāĻ āĻāĻ¨ā§āĻ āĻ¸āĻŽā§ āĻāĻ¸āĻŽāĻ¤āĻžāĻ° āĻĻā§āĻ āĻŦāĻž āĻ¤āĻ¤ā§āĻ§āĻŋāĻ āĻ¸ā§āĻā§āĻāĻŽā§āĻ¨ā§āĻ āĻĨā§āĻā§ āĻāĻāĻžāĻ¨āĻž āĻ°āĻžāĻļāĻŋāĻ° āĻŽāĻžāĻ¨ āĻŦā§āĻ° āĻāĻ°āĻžāĻ° āĻĻāĻ°āĻāĻžāĻ° āĻšā§āĨ¤ āĻāĻ¸āĻŦ āĻā§āĻˇā§āĻ¤ā§āĻ°ā§ āĻāĻŦāĻŋ āĻāĻāĻā§ āĻ¸āĻŽāĻžāĻ§āĻžāĻ¨ āĻāĻ°āĻžāĻ° āĻā§ā§āĻŋ āĻ¨ā§āĻāĨ¤ āĻāĻ¸āĻ˛ āĻāĻŋāĻāĻ°āĻ āĻĨā§āĻā§ āĻāĻ¸āĻž āĻāĻāĻāĻž āĻāĻā§āĻ āĻĻāĻŋā§ā§ āĻāĻĻāĻžāĻšāĻ°āĻŖ āĻĻā§āĻ, āĻŦā§āĻāĻ¤ā§ āĻ¸ā§āĻŦāĻŋāĻ§āĻž āĻšāĻŦā§āĨ¤ Sample Problem Â (From Real GRE) […]

## ã2.4.bã āĻĢāĻžāĻāĻļāĻ¨ āĻāĻŦāĻ āĻāĻ° āĻ¸āĻžāĻĨā§ āĻ¸āĻŽā§āĻĒāĻ°ā§āĻāĻŋāĻ¤ āĻŦāĻŋāĻ­āĻŋāĻ¨ā§āĻ¨ āĻŦāĻŋāĻˇā§āĻžāĻĻāĻŋāĻ° āĻĒā§āĻ°ā§āĻ¯āĻžāĻāĻāĻŋāĻ¸

[Math Center] 1. Ashley and Beatrice received the same score on a physical fitness test. The scores for this test, [latex]t[latex], are determined by the formula [latex]t=3ps-25m[latex] where [latex]s[latex] and [latex]p[latex] are the numbers of sit-ups and push-ups the athlete can do in one minute and [latex]m[latex] is the number of minutes she takes to […]

## ã2.3.bã āĻĻā§āĻŦāĻŋāĻāĻžāĻ¤ āĻ¸āĻŽā§āĻāĻ°āĻŖ āĻŦāĻŋāĻˇā§āĻ āĻĒā§āĻ°ā§āĻ¯āĻžāĻāĻāĻŋāĻ¸

[Math Center] 1. [latex]y ={ 2x }^{ 2 } +7x-3[latex] Quantity A Quantity B [latex]x[latex] [latex]y[latex]   2. [latex]\frac{ 1-x }{ x-1 }=\frac{ 1 }{ x }[latex] Quantity A Quantity B [latex]x[latex] [latex]-\frac{ 1 }{ 2 }[latex]   3. [latex](x+3)(y-4)=0[latex] Quantity A Quantity B [latex]xy[latex] [latex]-12[latex]   4. If both expressionsÂ [latex]{ x }^{ 2 }-3x+2[latex] […]

## ã2.2.bã āĻ¸āĻŽā§āĻāĻ°āĻŖ āĻāĻŦāĻ āĻ¸ā§āĻāĻ āĻŦāĻŋāĻˇā§āĻ āĻĒā§āĻ°ā§āĻ¯āĻžāĻāĻāĻŋāĻ¸

[Math Center] 1. If [latex]1+x+{ x }^{ 2 }+{ x }^{ 3 }=60[latex] then the average (arithmetic mean) of [latex]x,{ x }^{ 2 },{ x }^{ 3 },{ x }^{ 4 }[latex] is equal to which of the following? A [latex]12x[latex] B [latex]15x[latex]  C [latex]20x[latex]  D [latex]30x[latex]  E [latex]60x[latex]   2. [latex]0 […]

## ã2.1.bã āĻ¸āĻāĻā§āĻ¯āĻž āĻāĻ āĻ¨ āĻ āĻāĻā§āĻāĻā§āĻ˛ā§āĻ° āĻ¸ā§āĻĨāĻžāĻ¨ āĻŦāĻŋāĻ¨āĻŋāĻŽā§ āĻāĻāĻ¨āĻž āĻŦāĻŋāĻˇā§āĻ āĻ¸āĻŽāĻ¸ā§āĻ¯āĻž

[Math Center] 1. If [latex]2x=3y=4z=20[latex], then [latex]12xyz=[latex] A [latex]16,000[latex] B [latex]8,000[latex]  C [latex]4,000[latex]  D [latex]800[latex]  E [latex]10[latex]   2. [latex]0<x<y<1[latex] Quantity A Quantity B [latex]1-y[latex] [latex]y-x[latex]   3. [latex]st=\sqrt { 10 }[latex] Quantity A Quantity B [latex]{ s }^{ 2 }[latex] [latex]{ t }^{ 2 }[latex]   4. [latex]x <1[latex] [latex]x[latex]â [latex]0[latex] Quantity […]

## ã2.1.aãVariables related basics

Â [Math Center Home] [āĻ¨ā§āĻāĻ āĻāĻ āĻāĻ°ā§āĻāĻŋāĻā§āĻ˛āĻāĻŋ (2) Algebra āĻŦāĻŋāĻ­āĻžāĻā§āĻ°Â āĻāĻ§ā§āĻ¨ā§Â ã1ãAlgebra āĻā§āĻ¯āĻžāĻĒā§āĻāĻžāĻ°ā§āĻ° āĻāĻ¨ā§āĻ¤āĻ°ā§āĻāĻ¤, āĻ¯āĻžÂ ã2.1.aãāĻāĻŋāĻšā§āĻ¨ āĻĻāĻŋā§ā§ āĻĒā§āĻ°āĻāĻžāĻļ āĻāĻ°āĻž āĻšā§ā§āĻā§] ã2.1.aãVariables related basics Algebraic Translations āĻŦāĻŋāĻ­āĻŋāĻ¨ā§āĻ¨ āĻĒāĻ°ā§āĻā§āĻˇāĻžāĻ° āĻŽā§āĻ¯āĻžāĻĨ āĻ¸ā§āĻāĻļāĻ¨ā§ āĻĒāĻžāĻāĻŋāĻāĻŖāĻŋāĻ¤ āĻāĻžāĻ¤ā§ā§ āĻāĻ¨ā§āĻ āĻāĻā§āĻ āĻāĻ¸ā§ āĻ¯ā§āĻā§āĻ˛ā§ āĻāĻ¨ā§āĻ āĻ¸āĻŽā§ algebraic equation āĻāĻ° āĻ­āĻžāĻˇāĻžā§ āĻāĻ¨ā§āĻŦāĻžāĻĻ āĻāĻ°āĻžāĻ° āĻĻāĻ°āĻāĻžāĻ° āĻšā§āĨ¤ āĻ¯ā§āĻŽāĻ¨, âāĻĻā§āĻ āĻāĻāĻā§āĻ° āĻāĻāĻāĻŋ āĻ¸āĻāĻā§āĻ¯āĻž āĻ¸ā§āĻĨāĻžāĻ¨ āĻŦāĻŋāĻ¨āĻŋāĻŽā§ āĻāĻ°āĻ˛ā§â āĻŦāĻžāĻā§āĻ¯ āĻĨā§āĻā§ āĻāĻŽāĻ°āĻž āĻ§āĻ°ā§ āĻ¨āĻŋāĻ¤ā§ āĻĒāĻžāĻ°āĻŋ […]

## ã2.4.aãāĻĢāĻžāĻāĻļāĻ¨ āĻāĻŦāĻ āĻāĻ° āĻ¸āĻžāĻĨā§ āĻ¸āĻŽā§āĻĒāĻ°ā§āĻāĻŋāĻ¤ āĻŦāĻŋāĻ­āĻŋāĻ¨ā§āĻ¨ āĻŦāĻŋāĻˇā§āĻžāĻĻāĻŋ

[Math Center Home] [āĻ¨ā§āĻāĻ āĻāĻ āĻāĻ°ā§āĻāĻŋāĻā§āĻ˛āĻāĻŋ (2) Algebra āĻŦāĻŋāĻ­āĻžāĻā§āĻ°Â āĻāĻ§ā§āĻ¨ā§Â ã4ãFunctions āĻā§āĻ¯āĻžāĻĒā§āĻāĻžāĻ°ā§āĻ° āĻāĻ¨ā§āĻ¤āĻ°ā§āĻāĻ¤, āĻ¯āĻžÂ ã2.4.aãāĻāĻŋāĻšā§āĻ¨ āĻĻāĻŋā§ā§ āĻĒā§āĻ°āĻāĻžāĻļ āĻāĻ°āĻž āĻšā§ā§āĻā§] ã2.4.aãāĻĢāĻžāĻāĻļāĻ¨ āĻāĻŦāĻ āĻāĻ° āĻ¸āĻžāĻĨā§ āĻ¸āĻŽā§āĻĒāĻ°ā§āĻāĻŋāĻ¤ āĻŦāĻŋāĻ­āĻŋāĻ¨ā§āĻ¨ āĻŦāĻŋāĻˇā§āĻžāĻĻāĻŋ FUNCTIONS āĻŦāĻŋāĻˇā§āĻ āĻ¸āĻŽāĻ¸ā§āĻ¯āĻžāĻā§āĻ˛ā§ āĻāĻ¨ā§āĻāĻāĻž āĻāĻ¤āĻŋāĻĒā§āĻ°ā§āĻŦā§ āĻāĻ˛ā§āĻāĻ¨āĻž āĻāĻ°āĻžÂ sequence problem -āĻ° āĻŽāĻ¤ā§āĻāĨ¤ āĻāĻĻā§āĻ°āĻā§ āĻ¸āĻžāĻ§āĻžāĻ°āĻŖāĻ¤āĻ āĻāĻāĻ°ā§āĻāĻŋ āĻāĻā§āĻˇāĻ° [latex]f()[latex] āĻŦāĻž [latex]g()[latex] āĻāĻĨāĻŦāĻž āĻāĻ¨ā§āĻ¯ āĻā§āĻ¨ āĻāĻā§āĻˇāĻ°ā§āĻ° āĻĒāĻžāĻļā§ āĻāĻāĻāĻŋ āĻŦā§āĻ°āĻžāĻā§āĻā§āĻ° āĻŽāĻ§ā§āĻ¯ā§ variable [latex]x[latex] āĻā§ āĻŦāĻ¸āĻŋā§ā§ āĻāĻŦāĻ āĻ¤āĻžāĻ° āĻĄāĻžāĻ¨ […]

## ã2.5.aãāĻāĻ¸āĻŽāĻ¤āĻž āĻŦāĻŋāĻˇā§āĻ āĻāĻ˛ā§āĻāĻ¨āĻž

[Math Center Home] [āĻ¨ā§āĻāĻ āĻāĻ āĻāĻ°ā§āĻāĻŋāĻā§āĻ˛āĻāĻŋ (2) Algebra āĻŦāĻŋāĻ­āĻžāĻā§āĻ°Â āĻāĻ§ā§āĻ¨ā§Â ã5ãInequality āĻā§āĻ¯āĻžāĻĒā§āĻāĻžāĻ°ā§āĻ° āĻāĻ¨ā§āĻ¤āĻ°ā§āĻāĻ¤, āĻ¯āĻžÂ ã2.5.aãāĻāĻŋāĻšā§āĻ¨ āĻĻāĻŋā§ā§ āĻĒā§āĻ°āĻāĻžāĻļ āĻāĻ°āĻž āĻšā§ā§āĻā§] ã2.5.aãāĻāĻ¸āĻŽāĻ¤āĻž āĻŦāĻŋāĻˇā§āĻ āĻāĻ˛ā§āĻāĻ¨āĻž Equations āĻāĻ° āĻā§āĻˇā§āĻ¤ā§āĻ°ā§ āĻĻā§āĻāĻāĻŋ āĻ­āĻŋāĻ¨ā§āĻ¨ āĻ°āĻžāĻļāĻŋāĻ° āĻŽāĻ§ā§āĻ¯ā§ āĻ¸āĻŽāĻ¤āĻž āĻāĻŋāĻšā§āĻ¨ (=) āĻŦā§āĻ¯āĻŦāĻšā§āĻ¤ āĻšā§āĨ¤ āĻāĻ° āĻĒāĻ° āĻ¸ā§āĻāĻžāĻ¨ā§ āĻā§āĻ¨ variable āĻĨāĻžāĻāĻ˛ā§ āĻ¤āĻžāĻ° āĻŽāĻžāĻ¨ āĻāĻŽāĻ°āĻž āĻŦā§āĻ° āĻāĻ°āĻŋāĨ¤Â inequalities āĻāĻ°Â āĻā§āĻˇā§āĻ¤ā§āĻ°ā§ āĻ¸āĻŽāĻ¤āĻž āĻāĻŋāĻšā§āĻ¨ āĻŦā§āĻ¯āĻŦāĻšā§āĻ¤ āĻšā§ āĻ¨āĻž, āĻāĻŋāĻ¨ā§āĻ¤ā§ āĻŦā§āĻšāĻ¤ā§āĻ¤āĻ° (greater than) āĻŦāĻž āĻā§āĻˇā§āĻĻā§āĻ°āĻ¤āĻ° (smaller […]

## ã2.6.aãāĻ¸āĻŽāĻžāĻ¨ā§āĻ¤āĻ° āĻāĻŦāĻ āĻā§āĻŖā§āĻ¤ā§āĻ¤āĻ° āĻ§āĻžāĻ°āĻž

[Math Center Home] [āĻ¨ā§āĻāĻ āĻāĻ āĻāĻ°ā§āĻāĻŋāĻā§āĻ˛āĻāĻŋ (2) Algebra āĻŦāĻŋāĻ­āĻžāĻā§āĻ°Â āĻāĻ§ā§āĻ¨ā§Â ã6ãSeries and Sequences āĻā§āĻ¯āĻžāĻĒā§āĻāĻžāĻ°ā§āĻ° āĻāĻ¨ā§āĻ¤āĻ°ā§āĻāĻ¤, āĻ¯āĻžÂ ã2.6.aãāĻāĻŋāĻšā§āĻ¨ āĻĻāĻŋā§ā§ āĻĒā§āĻ°āĻāĻžāĻļ āĻāĻ°āĻž āĻšā§ā§āĻā§] ã2.6.aãāĻ¸āĻŽāĻžāĻ¨ā§āĻ¤āĻ° āĻāĻŦāĻ āĻā§āĻŖā§āĻ¤ā§āĻ¤āĻ° āĻ§āĻžāĻ°āĻž FORMULAS Formulas are another means by which theÂ  your ability is tasted to work with unknowns. Formulas are specific equations that can involve multiple variables. There are [latex]3[latex] major types of Formula problems […]