[Math Center] 1. Â If an athleteâs weight decreased from [latex]160[latex] pounds to [latex]152[latex] pounds, what was the percent decrease in the athleteâs 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. […]
Category: MC3: Number Properties
ã3.6.bã āĻ¸āĻāĻā§āĻ¯āĻžāĻ° āĻŦāĻŋāĻāĻžāĻā§āĻ¯āĻ¤āĻž āĻāĻŦāĻ āĻāĻāĻ āĻ¸ā§āĻĨāĻžāĻ¨ā§ā§ āĻŽāĻžāĻ¨ āĻŦāĻŋāĻˇā§āĻ āĻĒā§āĻ°ā§āĻ¯āĻžāĻāĻāĻŋāĻ¸
[Math Center] 1. When the positive integer [latex]n[latex] is divided by [latex]3[latex], the remainder is [latex]2[latex] and when [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. [latex]n[latex] is a positive integer that is divisible by [latex]6[latex]. Quantity A Quantity B The remainder when [latex]n[latex] is divided by [latex]12[latex] The […]
ã3.5.bã āĻ¸ā§āĻāĻ āĻāĻŦāĻ āĻŦāĻ°ā§āĻāĻŽā§āĻ˛ āĻŦāĻŋāĻˇā§āĻ āĻĒā§āĻ°ā§āĻ¯āĻžāĻāĻāĻŋāĻ¸
[Math Center] 1. Quantity A Quantity B [latex]\frac {{ 2 }^{ 30 }-{ 2 }^{ 29 }}{ 2 }[latex]  [latex]{ 2 }^{ 28 }[latex] 2. Quantity A Quantity B [latex]{ 3 }^{ x+1 }[latex]  [latex]{ 4 }^{ x }[latex] 3. [latex]x[latex] and [latex]m[latex] are positive numbers, and [latex]m[latex] is a multiple of [latex]3[latex]. […]
ã3.4.bã āĻ§āĻžāĻ°āĻžāĻŦāĻžāĻšāĻŋāĻ āĻ¸āĻāĻā§āĻ¯āĻž, āĻ¤āĻžāĻĻā§āĻ° āĻā§ āĻ āĻŽāĻ§ā§āĻ¯āĻŽāĻž āĻŦāĻŋāĻˇā§āĻ āĻĒā§āĻ°ā§āĻ¯āĻžāĻāĻāĻŋāĻ¸
[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 […]
ã3.3.bã āĻĒā§āĻ°āĻžāĻāĻŽ āĻŦāĻŋāĻˇā§āĻ āĻĒā§āĻ°ā§āĻ¯āĻžāĻāĻāĻŋāĻ¸
[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 […]
ã3.2.bã āĻ˛āĻ¸āĻžāĻā§ āĻāĻŦāĻ āĻāĻ¸āĻžāĻā§ āĻŦāĻŋāĻˇā§āĻ āĻĒā§āĻ°ā§āĻ¯āĻžāĻāĻāĻŋāĻ¸
[Math Center] 1. Quantity A Quantity B [latex]{ 950 }^{ 2000 }[latex]  [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. If [latex]\frac { 1 }{ \left( […]
ã3.1.bã āĻŦāĻŋāĻāĻŋāĻ¨ā§āĻ¨ āĻ§āĻ°āĻŖā§āĻ° āĻ¸āĻāĻā§āĻ¯āĻž, āĻ¸ā§āĻĨāĻžāĻ¨ā§ā§ āĻŽāĻžāĻ¨ āĻŦāĻŋāĻˇā§āĻ āĻĒā§āĻ°ā§āĻ¯āĻžāĻāĻāĻŋāĻ¸
[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) […]
ã3.3.aãāĻĒā§āĻ°āĻžāĻāĻŽ āĻ¸āĻŽā§āĻĒāĻ°ā§āĻāĻŋāĻ¤ āĻĒā§āĻ°āĻžāĻĨāĻŽāĻŋāĻ āĻ§āĻžāĻ°āĻŖāĻž āĻāĻŦāĻ āĻāĻŋāĻā§ āĻŦāĻŋāĻļā§āĻˇ āĻĒāĻĻā§āĻ§āĻ¤āĻŋ
 [Math Center Home] [āĻ¨ā§āĻāĻ āĻāĻ āĻāĻ°ā§āĻāĻŋāĻā§āĻ˛āĻāĻŋ (3) Number Properties āĻŦāĻŋāĻāĻžāĻā§āĻ°Â āĻ āĻ§ā§āĻ¨ā§Â ã3ãPrimes and Signed Numbers āĻā§āĻ¯āĻžāĻĒā§āĻāĻžāĻ°ā§āĻ° āĻ āĻ¨ā§āĻ¤āĻ°ā§āĻāĻ¤, āĻ¯āĻžÂ ã3.3.aãāĻāĻŋāĻšā§āĻ¨ āĻĻāĻŋā§ā§ āĻĒā§āĻ°āĻāĻžāĻļ āĻāĻ°āĻž āĻšā§ā§āĻā§] ã3.3.aãāĻĒā§āĻ°āĻžāĻāĻŽ āĻ¸āĻŽā§āĻĒāĻ°ā§āĻāĻŋāĻ¤ āĻĒā§āĻ°āĻžāĻĨāĻŽāĻŋāĻ āĻ§āĻžāĻ°āĻŖāĻž āĻāĻŦāĻ āĻāĻŋāĻā§ āĻŦāĻŋāĻļā§āĻˇ āĻĒāĻĻā§āĻ§āĻ¤āĻŋ Primes āĻŦāĻž āĻŽā§āĻ˛āĻŋāĻ āĻ¸āĻāĻā§āĻ¯āĻž A prime number is any positive integer larger than [latex]1[latex] with exactly two factors: [latex]1[latex] and itself. In other words, a prime number has NO factors […]
ã3.2.aãāĻ˛āĻ¸āĻžāĻā§ āĻāĻŦāĻ āĻāĻ¸āĻžāĻā§: āĻāĻ āĻāĻŋāĻāĻŦ āĻĒāĻĻā§āĻ§āĻ¤āĻŋ
[Math Center Home] [āĻ¨ā§āĻāĻ āĻāĻ āĻāĻ°ā§āĻāĻŋāĻā§āĻ˛āĻāĻŋ (3) Number Properties āĻŦāĻŋāĻāĻžāĻā§āĻ°Â āĻ āĻ§ā§āĻ¨ā§Â ã2ãFactors and multiplies: LCM,GCF āĻā§āĻ¯āĻžāĻĒā§āĻāĻžāĻ°ā§āĻ° āĻ āĻ¨ā§āĻ¤āĻ°ā§āĻāĻ¤, āĻ¯āĻžÂ ã3.2.aãāĻāĻŋāĻšā§āĻ¨ āĻĻāĻŋā§ā§ āĻĒā§āĻ°āĻāĻžāĻļ āĻāĻ°āĻž āĻšā§ā§āĻā§] ã3.2.aãāĻ˛āĻ¸āĻžāĻā§ āĻāĻŦāĻ āĻāĻ¸āĻžāĻā§: āĻāĻ āĻāĻŋāĻāĻŦ āĻĒāĻĻā§āĻ§āĻ¤āĻŋ Factors and Multiples Factors and Multiples are opposite of each other. Factor āĻšāĻ˛ā§ āĻāĻāĻāĻŋ positive integer āĻ¯āĻž āĻĻāĻŋā§ā§ āĻ āĻ¨ā§āĻ¯ āĻā§āĻ¨ integer āĻā§ āĻāĻžāĻ āĻāĻ°āĻž āĻ¯āĻžā§āĨ¤ [latex]1, 2, 4[latex] and [latex]8[latex] […]
ã3.1.aãāĻŦāĻŋāĻāĻŋāĻ¨ā§āĻ¨ āĻ§āĻ°āĻŖā§āĻ° āĻ¸āĻāĻā§āĻ¯āĻž, āĻ¸ā§āĻĨāĻžāĻ¨ā§ā§ āĻŽāĻžāĻ¨ āĻāĻŦāĻ āĻāĻŋāĻā§ āĻĒāĻĻā§āĻ§āĻ¤āĻŋ
[Math Center Home] [āĻ¨ā§āĻāĻ āĻāĻ āĻāĻ°ā§āĻāĻŋāĻā§āĻ˛āĻāĻŋ (3) Number Properties āĻŦāĻŋāĻāĻžāĻā§āĻ°Â āĻ āĻ§ā§āĻ¨ā§Â ã1ãTypes of Numbers āĻā§āĻ¯āĻžāĻĒā§āĻāĻžāĻ°ā§āĻ° āĻ āĻ¨ā§āĻ¤āĻ°ā§āĻāĻ¤, āĻ¯āĻžÂ ã3.1.aãāĻāĻŋāĻšā§āĻ¨ āĻĻāĻŋā§ā§ āĻĒā§āĻ°āĻāĻžāĻļ āĻāĻ°āĻž āĻšā§ā§āĻā§] ã3.1.aãāĻŦāĻŋāĻāĻŋāĻ¨ā§āĻ¨ āĻ§āĻ°āĻŖā§āĻ° āĻ¸āĻāĻā§āĻ¯āĻž, āĻ¸ā§āĻĨāĻžāĻ¨ā§ā§ āĻŽāĻžāĻ¨ āĻāĻŦāĻ āĻāĻŋāĻā§ āĻĒāĻĻā§āĻ§āĻ¤āĻŋ āĻāĻ āĻ¨āĻāĻ°ā§ āĻāĻ āĻ āĻ§ā§āĻ¯āĻžā§ā§āĻ° āĻ¸ā§āĻ¤ā§āĻ°āĻ¸āĻŽā§āĻš: āĻ¯ā§ āĻĄāĻŋāĻāĻŋāĻ āĻĒāĻ°ā§āĻ¯āĻ¨ā§āĻ¤ rounding up āĻāĻ°āĻ¤ā§ āĻšāĻŦā§ āĻ¤āĻžāĻ° āĻ āĻŋāĻ āĻĒāĻ°ā§āĻ° āĻĄāĻŋāĻāĻŋāĻā§āĻ° āĻĻāĻŋāĻā§ āĻ¨āĻāĻ° āĻĻāĻŋāĻ¤ā§ āĻšāĻŦā§āĨ¤ āĻ¯āĻĻāĻŋ āĻ¸ā§āĻāĻž [latex]4[latex] āĻŦāĻž āĻ¤āĻžāĻ° āĻāĻŽ āĻšā§, āĻ¤āĻžāĻšāĻ˛ā§ āĻ¸ā§āĻāĻžāĻā§ […]
ã3.4.aãāĻ§āĻžāĻ°āĻžāĻŦāĻžāĻšāĻŋāĻ āĻ¸āĻāĻā§āĻ¯āĻž, āĻ¤āĻžāĻĻā§āĻ° āĻā§ āĻ āĻŽāĻ§ā§āĻ¯āĻŽāĻž āĻ¨āĻŋāĻ°ā§āĻŖā§ āĻāĻŦāĻ āĻ āĻ¨ā§āĻ¯āĻžāĻ¨ā§āĻ¯
 [Math Center Home] [āĻ¨ā§āĻāĻ āĻāĻ āĻāĻ°ā§āĻāĻŋāĻā§āĻ˛āĻāĻŋ (3) Number Properties āĻŦāĻŋāĻāĻžāĻā§āĻ°Â āĻ āĻ§ā§āĻ¨ā§Â ã4ãConsecutive Number āĻā§āĻ¯āĻžāĻĒā§āĻāĻžāĻ°ā§āĻ° āĻ āĻ¨ā§āĻ¤āĻ°ā§āĻāĻ¤, āĻ¯āĻžÂ ã3.4.aãāĻāĻŋāĻšā§āĻ¨ āĻĻāĻŋā§ā§ āĻĒā§āĻ°āĻāĻžāĻļ āĻāĻ°āĻž āĻšā§ā§āĻā§] ã3.4.aãāĻ§āĻžāĻ°āĻžāĻŦāĻžāĻšāĻŋāĻ āĻ¸āĻāĻā§āĻ¯āĻž, āĻ¤āĻžāĻĻā§āĻ° āĻā§ āĻ āĻŽāĻ§ā§āĻ¯āĻŽāĻž āĻ¨āĻŋāĻ°ā§āĻŖā§ āĻāĻŦāĻ āĻ āĻ¨ā§āĻ¯āĻžāĻ¨ā§āĻ¯ âĸ Consecutive multiplies āĻā§āĻŦāĻ˛āĻŽāĻžāĻ¤ā§āĻ° integer āĻĻā§āĻŦāĻžāĻ°āĻž āĻāĻ āĻŋāĻ¤ āĻšā§āĨ¤ âĸ The arithmetic mean (average) and median and equal to the element in the set can be found by figuring out the […]
ã3.6.aãāĻ¸āĻāĻā§āĻ¯āĻžāĻ° āĻŦāĻŋāĻāĻžāĻā§āĻ¯āĻ¤āĻž āĻāĻŦāĻ āĻāĻāĻ āĻ¸ā§āĻĨāĻžāĻ¨ā§ā§ āĻŽāĻžāĻ¨ āĻ¨āĻŋāĻ°ā§āĻŖā§ā§āĻ° āĻĒāĻĻā§āĻ§āĻ¤āĻŋ
[Math Center Home] [āĻ¨ā§āĻāĻ āĻāĻ āĻāĻ°ā§āĻāĻŋāĻā§āĻ˛āĻāĻŋ (3) Number Properties āĻŦāĻŋāĻāĻžāĻā§āĻ°Â āĻ āĻ§ā§āĻ¨ā§Â ã6ãDivisibility, Last digit āĻā§āĻ¯āĻžāĻĒā§āĻāĻžāĻ°ā§āĻ° āĻ āĻ¨ā§āĻ¤āĻ°ā§āĻāĻ¤, āĻ¯āĻžÂ ã3.6.aãāĻāĻŋāĻšā§āĻ¨ āĻĻāĻŋā§ā§ āĻĒā§āĻ°āĻāĻžāĻļ āĻāĻ°āĻž āĻšā§ā§āĻā§] ã3.6.aãāĻ¸āĻāĻā§āĻ¯āĻžāĻ° āĻŦāĻŋāĻāĻžāĻā§āĻ¯āĻ¤āĻž āĻāĻŦāĻ āĻāĻāĻ āĻ¸ā§āĻĨāĻžāĻ¨ā§ā§ āĻŽāĻžāĻ¨ āĻ¨āĻŋāĻ°ā§āĻŖā§ā§āĻ° āĻĒāĻĻā§āĻ§āĻ¤āĻŋ āĻĻā§āĻāĻāĻŋ integer āĻāĻ° āĻ¯ā§āĻāĻĢāĻ˛ āĻŦāĻž āĻŦāĻŋā§ā§āĻāĻĢāĻ˛ āĻ¸āĻŦ āĻ¸āĻŽā§ āĻāĻ°ā§āĻāĻāĻŋ integer āĻšā§āĨ¤ āĻĻā§āĻāĻāĻŋ integer āĻāĻ° āĻā§āĻŖāĻĢāĻ˛ āĻ¸āĻŦāĻ¸āĻŽā§ āĻāĻ°ā§āĻāĻāĻŋ integer āĻšā§āĨ¤ āĻĻā§āĻāĻāĻŋ integer āĻāĻ° āĻāĻžāĻāĻĢāĻ˛ āĻ¨āĻ¤ā§āĻ¨ āĻāĻāĻāĻŋ integer āĻšāĻ¤ā§ āĻĒāĻžāĻ°ā§ āĻāĻŦāĻžāĻ° āĻāĻāĻāĻž fraction (āĻāĻā§āĻ¨āĻžāĻāĻļ) āĻšāĻ¤ā§ […]
ã3.6.a2ãāĻĻāĻļāĻŽāĻŋāĻāĻ¯ā§āĻā§āĻ¤ āĻ¸āĻāĻā§āĻ¯āĻžāĻ° āĻ¸āĻžāĻšāĻžāĻ¯ā§āĻ¯ā§ āĻ āĻ¨ā§āĻĒāĻžāĻ¤ āĻ āĻāĻžāĻāĻļā§āĻˇ āĻ¨āĻŋāĻ°ā§āĻŖā§
[Math Center Home] [āĻ¨ā§āĻāĻ āĻāĻ āĻāĻ°ā§āĻāĻŋāĻā§āĻ˛āĻāĻŋ (3) Number Properties āĻŦāĻŋāĻāĻžāĻā§āĻ°Â āĻ āĻ§ā§āĻ¨ā§Â ã6ãDivisibility, Last digit āĻā§āĻ¯āĻžāĻĒā§āĻāĻžāĻ°ā§āĻ° āĻ āĻ¨ā§āĻ¤āĻ°ā§āĻāĻ¤, āĻ¯āĻžÂ ã3.6.a2ãāĻāĻŋāĻšā§āĻ¨ āĻĻāĻŋā§ā§ āĻĒā§āĻ°āĻāĻžāĻļ āĻāĻ°āĻž āĻšā§ā§āĻā§] Rule: āĻā§āĻ¨ āĻ¸āĻāĻā§āĻ¯āĻžāĻā§ ([latex]p[latex]) āĻāĻ°ā§āĻāĻāĻŋ āĻāĻ¨ā§āĻāĻŋāĻāĻžāĻ° ([latex]d[latex]) āĻĻāĻŋā§ā§ āĻāĻžāĻ āĻāĻ°āĻ˛ā§ āĻāĻžāĻāĻļā§āĻˇ āĻŦāĻž remainder āĻšāĻŋāĻ¸āĻžāĻŦā§ [latex]r[latex] āĻāĻ° āĻŽāĻžāĻ¨ āĻ¸āĻ°ā§āĻŦāĻ¨āĻŋāĻŽā§āĻ¨ [latex]0[latex] āĻāĻŦāĻ āĻ¸āĻ°ā§āĻŦā§āĻā§āĻ [latex](d-1)[latex] āĻĒāĻ°ā§āĻ¯āĻ¨ā§āĻ¤ āĻšāĻŦā§āĨ¤ [latex]r[latex] āĻāĻ° āĻŽāĻžāĻ¨ [latex]d[latex] āĻŦāĻž āĻ¤āĻžāĻ° āĻŦā§ āĻšāĻ¤ā§ āĻĒāĻžāĻ°āĻŦā§ āĻ¨āĻžāĨ¤ āĻāĻĻāĻžāĻšāĻ°āĻŖ āĻ¸ā§āĻŦāĻ°ā§āĻĒ, āĻā§āĻ¨ āĻ¸āĻāĻā§āĻ¯āĻžāĻā§ [latex]13[latex] āĻĻāĻŋā§ā§ āĻāĻžāĻ āĻāĻ°āĻ˛ā§ āĻāĻžāĻāĻļā§āĻˇ […]
ã3.5.aãāĻ¸ā§āĻāĻ āĻāĻŦāĻ āĻŦāĻ°ā§āĻāĻŽā§āĻ˛ āĻ¸āĻŽā§āĻĒāĻ°ā§āĻāĻŋāĻ¤ āĻāĻ˛ā§āĻāĻ¨āĻž
 [Math Center Home] [āĻ¨ā§āĻāĻ āĻāĻ āĻāĻ°ā§āĻāĻŋāĻā§āĻ˛āĻāĻŋ (3) Number Properties āĻŦāĻŋāĻāĻžāĻā§āĻ°Â āĻ āĻ§ā§āĻ¨ā§Â ã5ãExponents and roots āĻā§āĻ¯āĻžāĻĒā§āĻāĻžāĻ°ā§āĻ° āĻ āĻ¨ā§āĻ¤āĻ°ā§āĻāĻ¤, āĻ¯āĻžÂ ã3.5.aãāĻāĻŋāĻšā§āĻ¨ āĻĻāĻŋā§ā§ āĻĒā§āĻ°āĻāĻžāĻļ āĻāĻ°āĻž āĻšā§ā§āĻā§] ã3.5.aãāĻ¸ā§āĻāĻ āĻāĻŦāĻ āĻŦāĻ°ā§āĻāĻŽā§āĻ˛ āĻ¸āĻŽā§āĻĒāĻ°ā§āĻāĻŋāĻ¤ āĻāĻ˛ā§āĻāĻ¨āĻž Increasing power cause positive fraction to decrease. āĻ§āĻ¨āĻžāĻ¤ā§āĻŽāĻ āĻāĻā§āĻ¨āĻžāĻāĻļāĻā§ āĻ¯āĻ¤ āĻā§āĻ power āĻ āĻāĻ¨ā§āĻ¨ā§āĻ¤ āĻāĻ°āĻž āĻšā§ āĻ¤āĻžāĻ° āĻŽāĻžāĻ¨ āĻ¤āĻ¤ āĻŦā§ āĻšā§ āĻāĻŦāĻ āĻŦā§ āĻšāĻ¤ā§ āĻšāĻ¤ā§ āĻ¸ā§āĻāĻŋ āĻ¸āĻ°ā§āĻŦā§āĻžāĻā§āĻ āĻĒāĻ°ā§āĻ¯āĻ¨ā§āĻ¤ āĻ¯ā§āĻ¤ā§ āĻĒāĻžāĻ°ā§ āĻāĻŋāĻ¨ā§āĻ¤ā§ āĻāĻŋāĻā§āĻ¤ā§āĻ […]