#### If a jar with water weighs 8kg. When 1/2 of the water is poured out, the jar and the remaining water weigh 4 3/4 kg. How much does the jar weighs?

Solution#1: Water + jar = 8 Half na si water + jar = 4.75 ilan ba yung half na water na tinapon? 8 - 4.75 = 3.25 kgs So, 3.25 kgs ay HALF ng WATER 6.5 kgs ay WHOLE or KABUOHAN ng WATER (J+W) - W = J 8 - 6.5 = 1.5 Solution#2: Jar + water = 8 J + W = 8 Eq1 J + 0.5 W = 4.75 Eq2 Combine Eq1 and Eq2 0.5(J + W = 8 ) Eq1 0.5J + 0.5W = 4 J + 0.5 W = 4.75 Eq2 0.5J = 0.75 J = 0.75/0.5 J = 1.5 kgs *** 1/2 = 0.5 4 3/4 = 4.75

#### There are 3 numbers whose sum is 54; one number is double and triple times greater than the other numbers, what are those numbers?

n + 2n + 3n = 54 6n = 54 n = 54/6 n = 9 2n = 2(9) = 18 3n = 2(9) = 27

#### What number when increased by 74 percent of itself will equal to 80?

100%n + 74%n = 80 174%n = 80 1.74n = 80 n = 80/1.74 n = 8000/174 n = 45.977 round-off 46

#### 0.25 is to 0.125 as to 1.25 is to ________

Solution#1 0.25 is to 0.125 as to 1.25 is to 0.25 : 0.125 = 1.25 : n 0.25×5 = 1.25 0.125×5 = 0.625 Solution#2 0.25 : 0.125 = 1.25 : n (0.125×1.25)/0.25 =0.625

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#### 2 is to 50 as 3.2 is to _________

Solution#1 2 : 50 = 3.2 : n (50×3.2)/2 = 80 Solution#2 2×25 = 50 3.2 × 25 = 80

#### Mary Grace is 25 years younger than her mother, In 4 years; Her Mother will be twice as old as Mary Grace. How old are they now?

Mary Grace is 25 years younger than her mother, In 4 years; Her Mother will be twice as old as Mary Grace. How old are they now? Let M be the age of mother Given: NOW +4yrs Mother M 2(M-21) MaGrc M-25 M-25+4 = M-21 M+4 = 2M - 42 4+42 = 2M-M 46 = M 46-25 = 21 Ans: 21, 46

#### What is the smallest positive number which, when you divided by 3, 4 or 5, will leave a remainder of 2?

LCM of 3,4,5, is 60, add 2 and the answer is 62

#### 44 is 80% of what number?

Let n be the number 44 = 80% × n 44 = 0.8 × n 44/0.8 = n 440/8 = n 55 = n

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#### 0.30 is to 0.075 as 0.15 is to ______

Solution#1 0.3 : 0.075 = 0.15 0.15×0.075 = 0.3 n 0.01125÷0.3 = 0.0375 Solution#2 0.3 : 0.075 = 0.15 : n 1000(0.3 : 0.075 = 0.15 : n) 300 : 75 = 150 : 1000n 300÷4=75 150÷4=37.5 37.5 ÷ 1000 = 0.0375

#### 14 is to 28 as 5 is to _________

Solution#1 14 : 28 = 5 : n 14×2 = 28 5×2 = 10 Solution#2 14 : 28 = 5 : n 28×5)/14 = 10

#### 18+ 3 × 3 + (54/3+ -68/-4) =

18+ 3 × 3 + (54/3+ -68/-4) = 18+ 3 × 3 + (18+ 17) = 18+ 3 × 3 + (35) = 18 + 9 + 35 = 62 Apply RULE of operation (PEMDAS or GEMDAS)

#### 1/3 is to 3/7 as 1/6 is to ________

Solution#1 1/3 : 3/7 = 1/6 : n 1/(3×2) = 1/6 3/(7×2) = 3/14 Solution#2 1/3 : 3/7 = 1/6 : n 3/7 × 1/6 = 1/3 × n 3/42 = 1/3 n 1/14 ÷ 1/3 = n 1/14 × 3/1 = 3/14

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#### 75% is to 1/2 as 45% is to ______

Solution#1 75% is to 1/2 as 45% is to 0.75 : 0.5 = 0.45 : n (0.75÷3)×2=0.5 (0.45÷3)×2=0.3 or 3/10 Solution#2 75% : 1/2 = 45% : n 1/2 ×0.45 = 0.75 n 0.225/0.75 = 0.3 or 3/10

#### 1/3 is to 2/18 as 1/12 is to ________

Solution: 1/3 : 2/18 = 1/12 : n 1/3 : 1/9 = 1/12 : n 1/9(1/12) = 1/3 n 1/108 ÷ 1/3 = n 1/108 × 3/1 = 3/108 = 1/36 1/36 is also 2/72 *Take note: 1/9 is the proper fraction of 2/18 which is only doubled Solution#2 1/3 : 2/18 = 1/12 : n 2/18 × 3/1 = 6/18 or 1/3 1/12 × 1/3 = 1/36 or 2/72

#### Which of the following numbers is represented by the prime factors 2 × 3 × 7?

Just multiply them 2×3×7 = 42

#### At 6:30 am, Rosalyn told Mendez that she found Rosalie 15 and ¼ hours ago, at what time Rosalyn found Rosalie?

6:30am – 12hrs = 6:30pm 6:30pm – (15.15hrs – 12hrs) = 3:15pm

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#### 483.43 + 123.334 + 31.5544 + 444.4 =

Please select 2 correct answers

Solution: Write down all the given numbers vertically and align all decimals, then you can add them. To shorten your time, check the 4th digit from the decimal point or the ten-thousandths place, it is 4. Then the 3rd digit from the decimal point or the thousandths place, you have 4+4 and it is 8. Eliminate choice A because the answer must be 1000+. You only have choice d that has 84 on the last two digits after the decimal.

#### 30% is to 3/5 as 80% is to ________

Solution#1 30% : 3/5 = 80% : n 0.3 : 0.6 = 0.8 : n 0.3 × 2 = 0.6 0.8 × 2 = 1.6 or 1 3/5 Solution#2 30% : 3/5 = 80% : n 0.3 : 3/5 = 0.8 : n (3/5 × 0.8) = 0.3 n 2.4/5 = 0.3n 0.48/0.3 = n 1.6 or 1 3/5

#### 4 × 8 + 12/4 - 8/2 =

Solution: 4 × 8 + 12/4 - 8/2 = 32 + 3 - 4 35 – 4 = 31 ---------------------------------

#### 2/5 is to 20% as ¾ is to ________

Solution#1 2/5 : 20% = 3/4 : n 0.4 : 0.2 = 0.75 : n 0.4 ÷ 2 = 0.2 0.75 ÷ 2 = 0.375 0.375×100% = 37.5% Solution#2 2/5 : 20% = 3/4 : n 2/5 : 0.2 = 3/4 0.2 (3/4) = 2/5 n 0.6/4 ÷ 2/5 = n 0.6/4 × 5/2 = 3/8 3/8 = 0.375×100% = 37.5%

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#### Square root of 0.000049

Solution#1: (Best solution) Convert to fraction.... ---> √(49/1,000,000) square root of 49 = 7 square root of 1,000,000 = 1000 7/1000 = 0.007 Soln#2: 0.000049 √49 = 7 Placement of decimal nasa pang-anim... divide to half, nasa pangatlo na ngayon.... Kaya ---> 0.007

#### Which is the greatest?

Eliminate all below halves, then compute the remaining by dividing numerators by denominators.

#### 3/8 is to 12/32 as 2/5 is to ________

Solution#1 3/8 : 12/32 = 2/5 : n 3/8 × 4/4 = 12/32 2/5 × 4/4 = 8/20 Solution#2 3/8 : 12/32 = 2/5 : n 3/8 : 3/8 = 2/5 3/8 × 2/5 = 3/8 × n 6/40 × 8/3 = n 3/20 × 8/3 = n 24/60 = 8/20

#### A special teacher has 400 units of 6% phosphoric acid solution, and an unlimited supply of 12% phosphoric acid solution. How many units of the latter must she add to the former to produce 10% phosphoric acid solution?

6% (400) + 12% n = 10% (400+n) 2400 + 12n = 4000 + 10n 12n – 10n = 4000 – 2400 2n = 1600 n = 1600/2 n = 800

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#### If 3 siomai cost P 15 pesos, how much if Kenneth buy 12 siomais.

12/3 = 4 × 15 = 60 Every 3 siomai cost 15 There are four 3’s in 12, so 4×15, answer is 60. You can also divide 15 by 3 equals 5 each and then multiply 5 × 12 = 60

#### 0.35 is to 7 as 0.45 is to ________

Solution#1 0.35 : 7 = 0.45 : n 0.35 × 20 = 7 0.45 × 20 = 9 Solution#2 0.35 : 7 = 0.45 : n (7× 0.45)/0.35 = n 3.15/0.35 = 9

#### 1 is to 1/4 as 5/25 is to ________

Solution#1 1 : 1/4 = 5/25 : n 1÷4 = ¼ 5/25 ÷ 4 = 1/5 ÷ 4 = 1/5 × 1/4 = 1/20 Solution#2 1 : 1/4 = 5/25 : n 5/25(1/4) = 1×n 5/100 = n 1/20 = n

#### 0.2 is to 0.4 as 0.3 is to ________

0.2 : 0.4 = 0.3 : n *Take note: look at the choices... if ur answer is NOT in the choices, then analyze again... 0.2 × (0.2×10) = 0.4 0.3 × (0.3×10) = 0.9

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#### 0.4 is to 2/5 as 0.6 is to ________

Solution#1 0.4 : 2/5 = 0.6 : n 0.4 is equivalent to 2/5. So, 0.6 = 6/10 or 3/5 Solution#2 0.4 : 2/5 = 0.6 : n 2/5 × 0.6 = 0.4 × n 0.24/0.4 = 0.6 0.6 = 6/10 or 3/5

#### 0.75 is to ¾ as 0.8 is to ______

Solution#1 0.75 is no doubt equals to 3/4 So, 0.8 is 8/10 or 4/5 Solutionn#2 0.75 : 3/4 = 0.8 : n 3/4 × 0.8 = 0.75 n 0.6/0.75 = 0.8 or 4/5

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