Philippine Science High School Entrance Exam Review | Math 1 | Reviewer for Incoming Grade 7

[Music] hi everyone i am teacher diane in today's lesson we are going to talk about whole numbers we will be discussing the answer to the following questions let us look at this example which of the following numbers is divisible by 5 and 9. first can we eliminate anything are the numbers all divisible by 5 yes a number is divisible by five if the last digit is either zero or five so we cannot eliminate next let's see if which of the numbers is divisible by nine again how do we do that we simply add the digits let's look at letter a three plus four seven plus three ten plus two twelve plus five 17 it is not divisible by 9 17 is not divisible by 9 x how about letter b 4 plus 6 10 plus ten is twenty again not divisible by nine next three plus seven ten plus eight eighteen plus 4 plus 5 that's 18 plus 9 and that is 27 27 is divisible by 9. so there you go that's our answer letter c given the number 83 200 1p in order for this number to be divisible by 3 6 and 9 p must be because divisibility rules by 3 6 and 9 they are related correct but first let me look at this divisible by 6 recall that if you are divisible by 6 you are divisible by 2 and 3 so that means p cannot be equal to 5 right because if the last digit here is 5 it cannot be divisible by 2 so that's eliminated so we're left with a c and d let us try a let us first add what we have over here the digits 2 plus 1 plus p we have 11 plus 213 plus 1 that's 14. 14 plus something it should be divisible by 3 and 9 can p be equal to 4 if p is equal to 4 then this will be 18 right and 18 is divisible by three and nine automatically it's also divisible by six its last digit is four it's divisible by two so if you're divisible by two and three you are also divisible by six so therefore our answer is letter a next mrs owen has 27 desks in her classroom she wants to put the same number of desks in each row with no desks left over how many rows could mrs owen make what kind of question is this this is just a matter of finding out which of these numbers can divide 27 right and what is the answer there the answer is letter b because 9 can divide 27 okay because it says here that there is no death left over so we need to say there should be no remainder pause this video and try to answer it by yourself assuming that you have already paused the video let's answer this this number here is divisible by is it divisible by four what's the divisibility rule for four again you just look at the last two digits is 54 divisible by 4 let us see no right you have a remainder of 2 so eliminate definitely this one cannot be divisible by 5 because its last digit is 4. usually when i am solving and i already eliminated the first two choices i always go to the last choice that's just my technique okay so let's see is this divisible by name and actually i would prefer to check that instead of checking if it's divisible by it because if you want to see if it's divisible by 8 you would have to check the last 3 digits and i do not want to divide okay so let's look at choice d we add the digits right check if the sum of the digits is divisible by nine so we have five plus eight thirteen plus two fifteen plus three eighteen plus 5 23 plus 4 27 there you go 27 is divisible by 9 so the answer is letter d for this one again pause the video and then come back to it after you have solved the problem assuming that you have already answered this let us now discuss so it says here that arlene has 210 mangoes containing the same number of mangoes then each of the following could be the number of mangoes per basket except okay which among these you can end up with 21 mangoes right because 210 is divisible by 21 so that means you have 10 baskets you cannot have 20 mangoes the answer is letter c 210 is not divisible by 20 because you would end up with a remainder of 10. a group of more than 10 and fewer than 20 students who pay the same amount for a class field trip if the total amount collected was 16 490 how many students were in the group so for this one we have no other option but to check which of these numbers can divide sixteen thousand four 490 the answer is letter c 17 16 490 when you divide it by 17 so look at this if you look at 164 it's already very close to 17 times 10 or 170 so i would be expecting that this is nine each of them paid 970 pesos if a number n is odd which of the following must also be r so what will we do here plug in specific numbers it says here that n is odd so get an odd number let's say one i always use one because on one is the smallest odd number which of the following must be odd so if n is equal to one what is n plus one this will be two and this is even letter b n over two will be equal to one half and it's not even it is not a whole number correct so no how about n plus two so this one will be one plus two three and this is uh we found the answer letter c if x is a whole number greater than 1 and the product of x and x plus 4 is odd then x must be in this case what we will do is use elimination we will try if letter a is the answer can x be even let's say x is 2 if x is 2 what is x plus four so when you substitute that would be two plus four so the answer is six but it says that the product let's look at the product the product of two and six is 12 but it says here that the product must be r so letter a cannot be the answer let's try b odd can x be an odd number let's say try one so if that's the case x plus four is five what is now the product one times five and the answer is odd answer is letter b what is the greatest common divisor of 54 36 and 24 what is greatest common divisor that is the same as gcf but instead of solving for the gcf you can just look at the choices all right so since we're looking for the greatest let us try nine we it's just a matter of checking if nine divides all of this but no right because nine cannot divide 24 how about six because then that's the next highest can six divide 54 yes can six divide 36 yes and six can divide 24 as well so the answer is letter c no computations needed right next lexi is making fruit baskets she has 20 apples and 8 oranges lexi wants to make all the fruit baskets identical without having any pieces of fruits left over what is the greatest number of fruit baskets lexi can make what kind of question is this it's just a matter of looking for the gcf of 20 and 8 what would that be the answer is letter c 4 because 4 is the greatest number that can divide both 20 and 8. for instance you did not know that it's a jcf question what you can do is you can just substitute the numbers here use elimination so if the answer is eight can there be eight baskets no because if you have eight baskets you cannot put the twenty apples there the marion identical number of fruits right it cannot be six also because you cannot put 20 apples in six baskets with having the identical number of apples okay so the answer is letter c three clocks ring once at the same time at 1 pm after that the first clock rings after every 90 minutes the second after 30 minutes and the third after every 60 minutes at what time will they again link together it's very important that you imagine what's going on so let's look at the first clock clock one it drinks after 90 minutes and then after another 90 minutes so that means 180 minutes has elapsed right and so on basically and so on for clock two every 30 minutes so at the end of 30 60 90 120 and so on clock 3 every 60 minutes so 61 20 180 240 and so on right at what time will they again link together can you imagine now what kind of problem is this we are looking for the lcm of 30 60 and 90. and what would that be whenever you're looking for the lcm of numbers 30 60 and 90 what i do is i look at the biggest number check for the multiples of that and see whether it is divisible by the other numbers so for example 90 is 90 divisible by 30 yes but 90 is not divisible by 60. what about 180 is 180 divisible by 60 yes it is also divisible by 30 180 minutes what is 180 minutes 180 minutes is 3 hours because this is 60 times three if they all started at 1 pm 1 pm after 3 hours so that's already 4 bm the answer is letter b if a number is divisible by 12 and 16 then the number must also be divisible by what number let's start with the smaller number if a number is divisible by both three and five then that means it is divisible also by 15. if it's divisible by 2 and 3 it's also divisible by 6 if it's let's say 4 and 10 is it divisible also by 40 is it automatic no the answer is that it is divisible by 20 what is the pattern that is going on here it is saying class that what are the relationships of these numbers these are the lcm 15 is the lcm of 3 and 5 6 is the lcm of 2 and 3 and 20 is the lcm of 4 and 10. going back to this we're just looking for the lcm of 12 and 16. how do you get the lcm so there are a lot of ways to get the lcm one of the ways is by looking at the prime factors right so for the prime factors 16 let's write the prime factor 3 this is 4 times 4 but they are not yet prime so 2 2 2 this is 4 times 3 and this is 2 2 so that means 16 is 2 times 2 times 2 times 2 right and then 12 is 2 times 2 times 3 here what is the lcm you bring down everything but make sure that you have the same number aligned so that's three times two times two times two times two this is sixteen times three so the answer is 48. so that's one method right for looking for the lcm so we're already here the lcm is 16 but what is the gcf you just look at the common so in this case the common would be this two and two here so the gcf is two times two it's 4 but of course it's easy to see that the gcf is 4 anyway another way to find the lcm is by doing continuous division think of a number which divides both 12 and 16. it doesn't have to be prime the bigger the better 4 and then divide 12 divided by 4 is 3. 16 divided by 4 is 4. for this one is there a number that can divide both three and four no more right so if that is the case this is already our last row what is now the lcm the lcm is the number here in the last row so that's four times three times four this is 12 times four you get 48. how many prime numbers are there between 70 and 80. so it's really just a matter of listing prime numbers so we have 71. it cannot be 72 72 is divisible by 3 right 73 we are just looking at the odd numbers there are candidates for prime numbers 75 no this is divisible by 577 this is divisible by 11 [Music] 79 yeah so the answer is letter e [Music] do [Music] so [Music] [Applause] [Music] you

Channel: MathHub TV

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Keywords: science high school entrance exam review, Philippine Science High School Entrance Exam Review, Reviewer for Incoming Grade 7, greatest common factor, least common multiple LCM, factors, prime numbers and composite numbers, odd and even numbers, philippine science high school, science high school entrance exam reviewer for grade 7 math, pshs review, pshs entrance exam reviewer, philippine science high school review, philippine science high school nce

Id: Iq_MRkH_oz4

Length: 21min 8sec (1268 seconds)

Published: Thu Jul 01 2021