ã4.1.bã āĻāĻ¨ā§āĻĒāĻžāĻ¤, āĻ¸āĻŽāĻžāĻ¨ā§āĻĒāĻžāĻ¤ āĻāĻŦāĻ āĻļāĻ¤āĻāĻ°āĻž āĻŦāĻŋāĻˇā§āĻ āĻĒā§āĻ°ā§āĻ¯āĻžāĻāĻāĻŋāĻ¸

[Math Center] 1. Â If an athleteâs weight decreased from [latex]160[latex] pounds to [latex]152[latex] pounds, what was the percent decrease in the athleteâs weight?   2. Emma spent $[latex]75[latex] buying a used bicycle and$[latex]27[latex] repairing it. Then she sold the bicycle for [latex]40[latex] percent more than the total amount she spent buying and repairing it. […]

ã3.6.bã āĻ¸āĻāĻā§āĻ¯āĻžāĻ° āĻŦāĻŋāĻ­āĻžāĻā§āĻ¯āĻ¤āĻž āĻāĻŦāĻ āĻāĻāĻ āĻ¸ā§āĻĨāĻžāĻ¨ā§ā§ āĻŽāĻžāĻ¨ āĻŦāĻŋāĻˇā§āĻ āĻĒā§āĻ°ā§āĻ¯āĻžāĻāĻāĻŋāĻ¸

[Math Center] 1. When the positive integerÂ [latex]n[latex] is divided by [latex]3[latex], the remainder isÂ [latex]2[latex] and whenÂ [latex]n[latex] is divided by [latex]5[latex], the remainder is [latex]1[latex]. What is the least possible value of [latex]n[latex]?   2.Â [latex]n[latex] is a positive integer that is divisible by [latex]6[latex]. Quantity A Quantity B The remainder whenÂ [latex]n[latex] is divided by [latex]12[latex] The […]

ã3.5.bã āĻ¸ā§āĻāĻ āĻāĻŦāĻ āĻŦāĻ°ā§āĻāĻŽā§āĻ˛ āĻŦāĻŋāĻˇā§āĻ āĻĒā§āĻ°ā§āĻ¯āĻžāĻāĻāĻŋāĻ¸

[Math Center] 1. Quantity A Quantity B [latex]\frac {{ 2 }^{ 30 }-{ 2 }^{ 29 }}{ 2 }[latex] Â [latex]{ 2 }^{ 28 }[latex]   2. Quantity A Quantity B [latex]{ 3 }^{ x+1 }[latex] Â [latex]{ 4 }^{ x }[latex]   3.Â  [latex]x[latex] and [latex]m[latex] are positive numbers, and [latex]m[latex] is a multiple of [latex]3[latex]. […]

ã3.4.bã āĻ§āĻžāĻ°āĻžāĻŦāĻžāĻšāĻŋāĻ āĻ¸āĻāĻā§āĻ¯āĻž, āĻ¤āĻžāĻĻā§āĻ° āĻā§ āĻ āĻŽāĻ§ā§āĻ¯āĻŽāĻž āĻŦāĻŋāĻˇā§āĻ āĻĒā§āĻ°ā§āĻ¯āĻžāĻāĻāĻŋāĻ¸

[Math Center] 1. [latex]r, s[latex], and [latex]t[latex] are three consecutive odd integers such that [latex]r<s<t[latex]. Quantity A Quantity B [latex]r+s+1[latex] Â [latex]s+t-1[latex]   2. By how much is the greatest of five consecutive even integers greater than the smallest among them? (A) [latex]1[latex] (B) [latex]2[latex] (C) [latex]4[latex] (D) [latex]8[latex] (E) [latex]10[latex]   3. Â Which one of […]

ã3.3.bã āĻĒā§āĻ°āĻžāĻāĻŽ āĻŦāĻŋāĻˇā§āĻ āĻĒā§āĻ°ā§āĻ¯āĻžāĻāĻāĻŋāĻ¸

[Math Center] 1. Quantity A Quantity B The number of prime numbers divisible by [latex]2[latex] The number of prime numbers divisible by [latex]3[latex]   2. Which one of the following equals the product of exactly two prime numbers? (A) [latex]11*6[latex] (B) [latex]13*22[latex] (C) [latex]14*23[latex] (D) [latex]17*21[latex] (E) [latex]13*23[latex]   3. Which one of the following […]

ã3.2.bã āĻ˛āĻ¸āĻžāĻā§ āĻāĻŦāĻ āĻāĻ¸āĻžāĻā§ āĻŦāĻŋāĻˇā§āĻ āĻĒā§āĻ°ā§āĻ¯āĻžāĻāĻāĻŋāĻ¸

[Math Center] 1. Quantity A Quantity B [latex]{ 950 }^{ 2000 }[latex] Â [latex]{ 10 }^{ 2000 }[latex]   2. Which of the following integers are multiples of both [latex]2[latex] and [latex]3[latex] ? Indicate all such integers. (A) [latex]8[latex] (B) [latex]9[latex] (C) [latex]12[latex] (D) [latex]18[latex] (E) [latex]21[latex] (F) [latex]36[latex]   3. IfÂ [latex]\frac { 1 }{ \left( […]

ã3.1.bã āĻŦāĻŋāĻ­āĻŋāĻ¨ā§āĻ¨ āĻ§āĻ°āĻŖā§āĻ° āĻ¸āĻāĻā§āĻ¯āĻž, āĻ¸ā§āĻĨāĻžāĻ¨ā§ā§ āĻŽāĻžāĻ¨ āĻŦāĻŋāĻˇā§āĻ āĻĒā§āĻ°ā§āĻ¯āĻžāĻāĻāĻŋāĻ¸

[Math Center] 1. Set [latex]S[latex] consists of all positive integers less than [latex]81[latex] that are not equal to the square of an integer. Quantity A Quantity B The number of integers in set [latex]S[latex] Â [latex]72[latex]   2. Which of the following numbers is farthest from the number [latex]1[latex] on the number line? (A) [latex]-10[latex] (B) […]

ã3.3.aãāĻĒā§āĻ°āĻžāĻāĻŽ āĻ¸āĻŽā§āĻĒāĻ°ā§āĻāĻŋāĻ¤ āĻĒā§āĻ°āĻžāĻĨāĻŽāĻŋāĻ āĻ§āĻžāĻ°āĻŖāĻž āĻāĻŦāĻ āĻāĻŋāĻā§ āĻŦāĻŋāĻļā§āĻˇ āĻĒāĻĻā§āĻ§āĻ¤āĻŋ

Â [Math Center Home] [āĻ¨ā§āĻāĻ āĻāĻ āĻāĻ°ā§āĻāĻŋāĻā§āĻ˛āĻāĻŋ (3)Â Number Properties āĻŦāĻŋāĻ­āĻžāĻā§āĻ°Â āĻāĻ§ā§āĻ¨ā§Â ã3ãPrimes and Signed Numbers āĻā§āĻ¯āĻžāĻĒā§āĻāĻžāĻ°ā§āĻ° āĻāĻ¨ā§āĻ¤āĻ°ā§āĻāĻ¤, āĻ¯āĻžÂ ã3.3.aãāĻāĻŋāĻšā§āĻ¨ āĻĻāĻŋā§ā§ āĻĒā§āĻ°āĻāĻžāĻļ āĻāĻ°āĻž āĻšā§ā§āĻā§] ã3.3.aãāĻĒā§āĻ°āĻžāĻāĻŽ āĻ¸āĻŽā§āĻĒāĻ°ā§āĻāĻŋāĻ¤ āĻĒā§āĻ°āĻžāĻĨāĻŽāĻŋāĻ āĻ§āĻžāĻ°āĻŖāĻž āĻāĻŦāĻ āĻāĻŋāĻā§ āĻŦāĻŋāĻļā§āĻˇ āĻĒāĻĻā§āĻ§āĻ¤āĻŋ PrimesÂ āĻŦāĻž āĻŽā§āĻ˛āĻŋāĻ āĻ¸āĻāĻā§āĻ¯āĻž A prime number is any positive integer larger thanÂ [latex]1[latex] with exactly two factors: [latex]1[latex] and itself. In other words, a prime number has NO factors […]

ã3.2.aãāĻ˛āĻ¸āĻžāĻā§ āĻāĻŦāĻ āĻāĻ¸āĻžāĻā§: āĻāĻ āĻāĻŋāĻāĻŦ āĻĒāĻĻā§āĻ§āĻ¤āĻŋ

[Math Center Home] [āĻ¨ā§āĻāĻ āĻāĻ āĻāĻ°ā§āĻāĻŋāĻā§āĻ˛āĻāĻŋ (3)Â Number Properties āĻŦāĻŋāĻ­āĻžāĻā§āĻ°Â āĻāĻ§ā§āĻ¨ā§Â ã2ãFactors and multiplies: LCM,GCF āĻā§āĻ¯āĻžāĻĒā§āĻāĻžāĻ°ā§āĻ° āĻāĻ¨ā§āĻ¤āĻ°ā§āĻāĻ¤, āĻ¯āĻžÂ ã3.2.aãāĻāĻŋāĻšā§āĻ¨ āĻĻāĻŋā§ā§ āĻĒā§āĻ°āĻāĻžāĻļ āĻāĻ°āĻž āĻšā§ā§āĻā§] ã3.2.aãāĻ˛āĻ¸āĻžāĻā§ āĻāĻŦāĻ āĻāĻ¸āĻžāĻā§: āĻāĻ āĻāĻŋāĻāĻŦ āĻĒāĻĻā§āĻ§āĻ¤āĻŋ Factors and Multiples Factors and Multiples are opposite of each other. Factor āĻšāĻ˛ā§ āĻāĻāĻāĻŋ positive integer āĻ¯āĻž āĻĻāĻŋā§ā§ āĻāĻ¨ā§āĻ¯ āĻā§āĻ¨ integer āĻā§ āĻ­āĻžāĻ āĻāĻ°āĻž āĻ¯āĻžā§āĨ¤ [latex]1, 2, 4[latex] and [latex]8[latex] […]

ã3.1.aãāĻŦāĻŋāĻ­āĻŋāĻ¨ā§āĻ¨ āĻ§āĻ°āĻŖā§āĻ° āĻ¸āĻāĻā§āĻ¯āĻž, āĻ¸ā§āĻĨāĻžāĻ¨ā§ā§ āĻŽāĻžāĻ¨ āĻāĻŦāĻ āĻāĻŋāĻā§ āĻĒāĻĻā§āĻ§āĻ¤āĻŋ

[Math Center Home] [āĻ¨ā§āĻāĻ āĻāĻ āĻāĻ°ā§āĻāĻŋāĻā§āĻ˛āĻāĻŋ (3)Â Number Properties āĻŦāĻŋāĻ­āĻžāĻā§āĻ°Â āĻāĻ§ā§āĻ¨ā§Â ã1ãTypes of Numbers āĻā§āĻ¯āĻžāĻĒā§āĻāĻžāĻ°ā§āĻ° āĻāĻ¨ā§āĻ¤āĻ°ā§āĻāĻ¤, āĻ¯āĻžÂ ã3.1.aãāĻāĻŋāĻšā§āĻ¨ āĻĻāĻŋā§ā§ āĻĒā§āĻ°āĻāĻžāĻļ āĻāĻ°āĻž āĻšā§ā§āĻā§] ã3.1.aãāĻŦāĻŋāĻ­āĻŋāĻ¨ā§āĻ¨ āĻ§āĻ°āĻŖā§āĻ° āĻ¸āĻāĻā§āĻ¯āĻž, āĻ¸ā§āĻĨāĻžāĻ¨ā§ā§ āĻŽāĻžāĻ¨ āĻāĻŦāĻ āĻāĻŋāĻā§ āĻĒāĻĻā§āĻ§āĻ¤āĻŋ āĻāĻ āĻ¨āĻāĻ°ā§ āĻāĻ āĻāĻ§ā§āĻ¯āĻžā§ā§āĻ° āĻ¸ā§āĻ¤ā§āĻ°āĻ¸āĻŽā§āĻš: āĻ¯ā§ āĻĄāĻŋāĻāĻŋāĻ āĻĒāĻ°ā§āĻ¯āĻ¨ā§āĻ¤ rounding up āĻāĻ°āĻ¤ā§ āĻšāĻŦā§ āĻ¤āĻžāĻ° āĻ āĻŋāĻ āĻĒāĻ°ā§āĻ° āĻĄāĻŋāĻāĻŋāĻā§āĻ° āĻĻāĻŋāĻā§ āĻ¨āĻāĻ° āĻĻāĻŋāĻ¤ā§ āĻšāĻŦā§āĨ¤ āĻ¯āĻĻāĻŋ āĻ¸ā§āĻāĻž [latex]4[latex] āĻŦāĻž āĻ¤āĻžāĻ° āĻāĻŽ āĻšā§, āĻ¤āĻžāĻšāĻ˛ā§ āĻ¸ā§āĻāĻžāĻā§ […]

ã3.4.aãāĻ§āĻžāĻ°āĻžāĻŦāĻžāĻšāĻŋāĻ āĻ¸āĻāĻā§āĻ¯āĻž, āĻ¤āĻžāĻĻā§āĻ° āĻā§ āĻ āĻŽāĻ§ā§āĻ¯āĻŽāĻž āĻ¨āĻŋāĻ°ā§āĻŖā§ āĻāĻŦāĻ āĻāĻ¨ā§āĻ¯āĻžāĻ¨ā§āĻ¯

Â [Math Center Home] [āĻ¨ā§āĻāĻ āĻāĻ āĻāĻ°ā§āĻāĻŋāĻā§āĻ˛āĻāĻŋ (3)Â Number Properties āĻŦāĻŋāĻ­āĻžāĻā§āĻ°Â āĻāĻ§ā§āĻ¨ā§Â ã4ãConsecutive Number āĻā§āĻ¯āĻžāĻĒā§āĻāĻžāĻ°ā§āĻ° āĻāĻ¨ā§āĻ¤āĻ°ā§āĻāĻ¤, āĻ¯āĻžÂ ã3.4.aãāĻāĻŋāĻšā§āĻ¨ āĻĻāĻŋā§ā§ āĻĒā§āĻ°āĻāĻžāĻļ āĻāĻ°āĻž āĻšā§ā§āĻā§] ã3.4.aãāĻ§āĻžāĻ°āĻžāĻŦāĻžāĻšāĻŋāĻ āĻ¸āĻāĻā§āĻ¯āĻž, āĻ¤āĻžāĻĻā§āĻ° āĻā§ āĻ āĻŽāĻ§ā§āĻ¯āĻŽāĻž āĻ¨āĻŋāĻ°ā§āĻŖā§ āĻāĻŦāĻ āĻāĻ¨ā§āĻ¯āĻžāĻ¨ā§āĻ¯ âĸ Consecutive multipliesÂ āĻā§āĻŦāĻ˛āĻŽāĻžāĻ¤ā§āĻ° integer āĻĻā§āĻŦāĻžāĻ°āĻž āĻāĻ āĻŋāĻ¤ āĻšā§āĨ¤ âĸ The arithmetic mean (average) and median and equal to the element in the set can be found by figuring out the […]

ã3.6.aãāĻ¸āĻāĻā§āĻ¯āĻžāĻ° āĻŦāĻŋāĻ­āĻžāĻā§āĻ¯āĻ¤āĻž āĻāĻŦāĻ āĻāĻāĻ āĻ¸ā§āĻĨāĻžāĻ¨ā§ā§ āĻŽāĻžāĻ¨ āĻ¨āĻŋāĻ°ā§āĻŖā§ā§āĻ° āĻĒāĻĻā§āĻ§āĻ¤āĻŋ

[Math Center Home] [āĻ¨ā§āĻāĻ āĻāĻ āĻāĻ°ā§āĻāĻŋāĻā§āĻ˛āĻāĻŋ (3)Â Number Properties āĻŦāĻŋāĻ­āĻžāĻā§āĻ°Â āĻāĻ§ā§āĻ¨ā§Â ã6ãDivisibility, Last digit āĻā§āĻ¯āĻžāĻĒā§āĻāĻžāĻ°ā§āĻ° āĻāĻ¨ā§āĻ¤āĻ°ā§āĻāĻ¤, āĻ¯āĻžÂ ã3.6.aãāĻāĻŋāĻšā§āĻ¨ āĻĻāĻŋā§ā§ āĻĒā§āĻ°āĻāĻžāĻļ āĻāĻ°āĻž āĻšā§ā§āĻā§] ã3.6.aãāĻ¸āĻāĻā§āĻ¯āĻžāĻ° āĻŦāĻŋāĻ­āĻžāĻā§āĻ¯āĻ¤āĻž āĻāĻŦāĻ āĻāĻāĻ āĻ¸ā§āĻĨāĻžāĻ¨ā§ā§ āĻŽāĻžāĻ¨ āĻ¨āĻŋāĻ°ā§āĻŖā§ā§āĻ° āĻĒāĻĻā§āĻ§āĻ¤āĻŋ āĻĻā§āĻāĻāĻŋ integer āĻāĻ° āĻ¯ā§āĻāĻĢāĻ˛ āĻŦāĻž āĻŦāĻŋā§ā§āĻāĻĢāĻ˛ āĻ¸āĻŦ āĻ¸āĻŽā§ āĻāĻ°ā§āĻāĻāĻŋ integer āĻšā§āĨ¤ āĻĻā§āĻāĻāĻŋÂ integer āĻāĻ° āĻā§āĻŖāĻĢāĻ˛ āĻ¸āĻŦāĻ¸āĻŽā§ āĻāĻ°ā§āĻāĻāĻŋÂ integer āĻšā§āĨ¤ āĻĻā§āĻāĻāĻŋÂ integer āĻāĻ° āĻ­āĻžāĻāĻĢāĻ˛ āĻ¨āĻ¤ā§āĻ¨ āĻāĻāĻāĻŋÂ integer āĻšāĻ¤ā§ āĻĒāĻžāĻ°ā§ āĻāĻŦāĻžāĻ° āĻāĻāĻāĻž fraction (āĻ­āĻā§āĻ¨āĻžāĻāĻļ) āĻšāĻ¤ā§ […]