# LET Reviewer General Education GenEd: Mathematics Part 1

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Below is the LET Reviewer for General Education GENED: Mathematics Part 1. We encourage readers/ reviewees to use the comment boxes after the article for discussion.

1. Two buses leave the same station at 8:00 pm. One bus travels north at the rate of 30 kph and the other travels east at 40 kph. How many kilometers apart are the buses at 10 pm?
a. 140 km
b. 100 km
c. 70 km
d. 50 km

2. Calculate the mean absolute deviation of the following numbers: 60, 80, 100, 75 and 95
a. 12.4
b. 14.2
c. 16.1
d. 18.9

3. Which of the following is the factorization of the binomial x2 - 42?
a. (x + 4)(x + 2)
b. (x – 4)2
c. x(x + 2x + 2)
d. (x – 4)(x + 4)

4. What value of x will satisfy the equation: 0.4(5x - 1470) = x?
a. 490
b. 2,130
c. 1470

5. Which of the following has the greatest value:
a. 3 + 32 + (3 + 3)2
b. 33
c. [(3 + 3)2]2
d. (3 + 3 + 3)2
6. The average of 5 different counting numbers is 20. What is the highest possible value that one of the numbers can have?
a. 20
b. 40
c. 30
d. 90

7. Three brothers inherited a cash amount of P62,000 and they divided it among themselves in the ratio of 5:4:1. How much more is the largest share than the smallest share?
a. P75,000
b. P30,000
c. P24,800

8. What is the missing terms in the series 5, 20, 80, ___,1280, ___, 20, 480?
a. 50;210
b. 40;160
c. 35;135
d. 320;5120

9. At what rate per annum should P2400 be invested so that it will earn an interest of P800 in 8 years?
a. 6 ½ %
b. 5 ½ %
c. 4.17 %
d. 6 %

10. The area of a rectangle is (x2 + 2x - 8). If its length is x + 4, what is its width?
a. x + 2
b. x - 2
c. x + 1
d. x + 6

11. What is the value of 12⅙ - 3 ⅜ - 5 ⅔ + 20 ¾?
a. 21 1/8
b. 22
c. 23 7/8
d. 21

12. The vertex angle of an isosceles triangle is 20°. What is the measure of one of the base angles?
a. 150°
b. 60°
c. 75°
d. 80°

13. Ana and Beth do a job together in three hours. Working alone, Ana does the job in 5 hours. How long will it take Beth to do the job alone?
a. 3 and 1/3 hours
b. 2 and 1/3 hours
c. 3 hours
d. 7 and 1/2 hours

14. How much greater is the sum of the first 50 counting numbers greater than the sum of the first 100 counting numbers?
a. 110
b. 3,775
c. 3,155
d. 1200

15. Which of the following has the largest value?
a. 85
b. 39
c. 65
d. 94

16.  A water tank contains 18 liters when it is 20% full. How many liters does it contain when 50% full?
a. 60
b. 30
c. 58
d. 45

17. The edges of a rectangular solid have these measures: 1.5 feet by 1½ feet by 3 inches. What is its volume in cubic inches?
a. 324
b. 225
c. 972
d. 27

18. In a certain school, the ratio of boys to girls is 5 is to 7. If there are 180 boys and girls in the school, how many boys are there?
a. 105
b. 90
c. 45
d. 75

19. Ruben’s grades in 6 subjects are 88, 90, 97, 90, 91 and 86? What is the least grade that he should aim for in the 7th subject if he has to have an average of 88?
a. 92
b. 74
c. 88
d. 85

20. On a certain day, three computer technicians took turns in manning a 24-hour internet shop. The number of hours Cesar, Bert, and Danny were on duty was in the ratio 3:4:5, respectively. The shop owner pays them P50 per hour. How much would Danny receive for that day?
a. P 230
b. P500
c. P160
d. P480

21. A retailer buys candies for P90.25. The pack has 35 pieces of candies. If she sells each candy for P2.25, how much profit does she make?
a. P11.50
b. P56.25
c. P37.50
d. P18.75

22. An online shop sells a certain calculator for P950 and charges P150 for shipping within Manila, regardless of the number of calculators ordered. Which of the following equations shows the total cost (y) of an order as a function of the number of calculators ordered (x)?
a. y = (950 + 150)x
b. y = 150x +950
c. x = 950y + 150
d. y = 950x + 150

23. One side of a 45° - 45° - 90° triangle measures x cm. What is the length of its hypotenuse?
a. X √3 cm
b. X cm
c. (X √3)/2 cm
d. X √2 cm

24. The legs of one right triangle are 9 and 12, while those of another right triangle are 12 and 16. How much longer is the perimeter of the larger triangle than the perimeter of the smaller triangle?
a. 84
b. 7
c. 12
d. 14

25. Determine the midpoint of the line segment joining the points (7, -3) and (-1, 6).
a. (2, 3/2)
b. (2, -3/2)
c. (3, 3/2)
d. (1, 5/2)

26. Which of these has the longest perimeter?
a. A square 21 cm on a side
b. A rectangle 19 cm long and 24 cm wide
c. An equilateral triangle whose side is 28 cm
d. A right triangle whose two legs are 24 and 32 cm

27.  How many square inches are in 2 square yard?
a. 900
b. 144
c. 1296
d. 2,592

28. In a playground for Kindergarten kids, 18 children are riding tricycles or bicycles. If there are 43 wheels in all, how many tricycles are there?
a. 8
b. 9
c. 7
d. 11

29. Nelia takes ¾ hour to dress and get ready for school. It takes 4/5 hour to reach the school. If her class starts promptly at 8:00 am; what is the latest time she can jump out of bed in order not to be late for school?
a. 6:42 am
b. 6:27 am
c. 6:57 am
d. 7:02 am

30. Which common fraction is equivalent to 0.215?
a. 43/200
b. 27/125
c. 21/50
d. 108/375

Answers: 1B 2A 3D 4D 5C 6D 7C 8D 9C 10B 11C 12D 13D 14 15A 16D 17C 18D 19B 20B 21 22D 23D 24C 25C 26D 27D 28C 29B 30A

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##### 96 comments:
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1. Answers key plz tnx

1. AnonymousJuly 27, 2017

nasa pinaka last po yung answers

2. wala po bang answer key?

3. Answer key please

4. Answer to number 14 is B. 3,775

Using Gauss formula... the sum of 1 to n = n(n+1)/ 2

1 to 50 = 50(50+1)/2 = 1275
1 to 100 = 100(100+1)/2 = 5050
So, 5050 - 1275 = 3,775

1. May God bless you!!!!!

5. Ano po answer dun sa number 14 at number 21?

1. AnonymousMay 16, 2017

14 B
21 A

2. hey, ask ko lang po .. san ba mkikita mga part 2 neto ?

3. 21 walang sagot error.
binili nya ang candy sa halagang P90.25
then 35 lahat ng candy sa isang pack. tapos binenta nya ng tig P2.25 each
so 35 * P2.25 = P78.75
P78.75 lang kita nya so wala siyang profit luge pa sya ng P11.25 kaya error.
ang tanong kasi magkano profit nya.

6. panu po nakuha ung number 1? bakit po B ang answer?
Thank you

1. Daisyrie VasquezMay 22, 2017

First, you have to get each other's distance after 2 hours:
North: d=st=30(2)=60
East: d=st=40(2)=80
Then, you have to apply Pythagorean Theorem in order to get the distance r^2 = a^2 + b^2 = 60^2 + 80^2 = 3600 + 6400=10 000
Get the square root of 10, 000 to get r= 100 km.

7. sa number 27 po, pano po nakuha?
thank you

1. 1 yard = 36 inches
1 yard^2 = 1296 inches^2
2 yard^2 = 2592 in^2

or,
2 yards = 72 inches
(2 yards = 72 in)^2
4 yards^2 = 5184 in^2
2 yards^2 = 2592

8. 4. What value of x will satisfy the equation: 0.4(5x - 1470) = x? a. 490 b. 2,130 c. 1470
ang naka-indicate po na answer ay D. pero wla po sa choices
x=588 tama po?

1. AnonymousJune 23, 2017

sa number 4 po ba ganito po ba process ng pag solve? distribution property, then transpose po.
kasi po wala pong nakaindicate na choices D po.
0.4(5x-1470)=x
0.4(5x)-0.4(1470)=x
2x-588=x
2x=588
2x/2=588/2
x=294

2. AnonymousJuly 11, 2017

588 po. di nyo na po na subtract ung isang x resulting to divide 588 by 2 which is wrong.

3. Hello po what is the right solution po sa # 4 ? salamat po sa maka ka sagot.

4. 0.4(5x-1470)=x
0.4(5x)-0.4(1470)=x
2x-588=x (TRANSFER X AND -500 AND CHANGE SIGNS)
2X-X=588
X=588

9. #21. A retailer buys candies for P90.25. The pack has 35 pieces of candies. If she sells each candy for P2.25, how much profit does she make?
2.25*35=78.75
90-78.75=11.25

But suppose to be the price of each candy is more than 2.50 or 2.60 because
90.25/35=2.5785714 or 2.58

10. Pano po nakuha yung sagot sa no. 1? Solution please thanks

1. using Pythagorean theorem

2. solution po sa number 1?

3. AnonymousMay 05, 2017

8:00 pm they start to part ways, and the question is how many kilometers apart after 10:00 pm, so the one that traveling north with a rate of 30kph (kilometer per Hour)using that rate we multiply it by two because the difference of 8:00 and 10:00 is 2hours. so the distance of the bus that traveling north from the starting point is 60km. the same thing with the bus that travels east, multiply it and it obtain 80km far from the starting point. so not using an illustration you form a right angle. to get the distance of the two, use the pythagorean theorem (c^2 = a^2 +b^2)

Let a = distance of bus traveling north from the starting point which is 60km
and b = distance of bus traveling east from the starting point which is 80km

c^2 = 60^2 + 80^2
then you'll obtain the distance of 100km

4. paano po basahin yun ^ na ito? anu po siya s math?

5. mga sir at mam,

pa help na po s mga number na ito

number - 3,4, 5, 8, 10, 11, 12, 15, 16, 18, 21, 22, 23, 25, 26, 29, 30.

solution and answer po

11. AnonymousMay 01, 2017

At what rate per annum should P2400 be invested so that it will earn an interest of P800 in 8 years?ano po ba ang solution nito

1. AnonymousJune 09, 2017

800/8 years = 100 yearly interest
To get its interest rate,
100/2,400 = 4.17%

2. 9. At what rate per annum should P2400 be invested so that it will earn an interest of P800 in 8 years?
a. 6 ½ %
b. 5 ½ %
c. 4.17 %
d. 6 %

solution:
principal(P) = 2,400
time (t) = 8 years
interest = 800
rate (r) = ?

formula: I=Prt

800 = 2400(r) (8)
800 = 2400 (8) r
800 = 19200 r
800/19200 = r
0.041666 = r
0.041666 (100) = r

Answer : 4.17% =r

12. AnonymousMay 25, 2017

Paano po yung number 11. Na stuck ako e. Maraming salamat po sa sasagot!

1. AnonymousJuly 08, 2017

Try mong gawing decimal ung my fraction...halimbawa dun sa dulo...20 3/4 gawin mong 20.75......3 devide 4 is 0.75....gawin mo rin dun sa iba makukuha mo na sagot

13. AnonymousMay 30, 2017

ano po ang answer Ng no.14 and 21

14. Ano po answer sa Number 4? :) salamat sa reply.

15. AnonymousJuly 07, 2017

Pano po yung shortcut ngpagsolve sa number 14?

16. AnonymousJuly 11, 2017

Ano po ung solution sa 2 ..

1. Mean Absolute Deviation (MAD) is simply calculating the positive distance (absolute value) of the mean from each data point and divided by the number of data points.

In No. 2 , the data points are 60, 80, 100, 75, & 95
The number of data points is 5.
To get the mean, simple add all the data points and then divide by the number of data points. (Parang averaging lang)
Mean = 60+80+100+75+95 = 410/5 = 82
Then the positive (absolute distance of the mean from each data points:
| 60 - 82 | = 22
| 80 - 82 | = 2
| 100 - 82 | = 18
| 75 - 82 | = 7
| 95 - 82 | = 13

Then add all the distances and divide by the number of data points
MAD = 22+2+18+7+13 = 62/5 = 12.40 Letter A

17. AnonymousJuly 11, 2017

Ung easy way solution po ng mga deviation? Slamat po

18. AnonymousJuly 21, 2017

Parang mali po ung answer sa number 19???

1. 19. Ruben’s grades in 6 subjects are 88, 90, 97, 90, 91 and 86? What is the least grade that he should aim for in the 7th subject if he has to have an average of 88?

(88+90+97+90+91+86+x)/7 = 88
(542+x)/7 = 88
542+x=88*7
x=616-542
x=74

a. 92
b. 74
c. 88
d. 85

19. This comment has been removed by the author.

20. how po 17?

1. No. 17...Volume in cubic inches

Given: 1.5 feet by 1 1/2 feet by 3 inches

The formula of volume is side x side x side (or edge x edge x edge)
Since the volume is to be in the form cubic inches, we need to convert all the measurement in inches:
1.5 feet = 1.5 x 12 inches = 18 inches
1 1/2 feet is the same as 1.5 feet = 18 inches
3 inches is already in inches
Then just multiply the measurements = 18x18x 3 = 972 cubic inches

21. pwede nnyo e show youe solution lahay sa nakaka alam ng mga sagot. wala na po kasi akong idea pa help naman po

22. paano pa ung mean absolute deviation? sa no.2 po

23. 60+80+100+75+95=410/5=82
60 of 82 = 22
80 of 82 = 2
100 of 82 = 18
75 of 82 = 7
95 of 82 = 13

22+2+18+7+13=62/5=12.4

24. Sa #14 anu po yung sagot? Thanks

25. Pano ung solution sa #6?

1. # 6 ==> 5 different counting numbers, the average is 100, what is possible highest number of one number?
Trial and error po.

First determine the total of the 5 numbers.
Since the average is 20, it suggests that the total of the 5 numbers is 100 ( because 100/5 = 20)
If we try 90, the total of the remaining 4 numbers should equal 10 ( 100 - 90 = 10)
Find 4 different numbers that totals 10 ==> 1, 2, 3, & 4 = 10
So the 90 is the highest possible number of one number in the group.

2. sir ano solution ng # 28&29?

3. solution Number 28
3T+2B=43 assuming no kids have trainng wheels on bicycles.

T+B=18 assume each bike and trike has only one kid on it.

3T+2(18-T)=43
T=43-36=7

26. Paano kinuha yung 24

1. First, you have to solve for the hypotenuse of both triangles.
Let x be the hypotenuse of the smaller triangle
y be the hypotenuse of the larger triangle
by Pythagorean theorem:
x=√[(9^2)+(12^2)]
x=15

y=√[(12^2)+(16^2)]
y=20

Then subtract the perimeter of the smaller triangle from the larger triangle
(12+16+y)-(9+12+x)
(12+16+20)-(9+12+15)
48-36
12

27. Pano po yung number 20? Nahihirapan na po kasi ako pag yung ratio talo talo na xD Salamat :D

1. add mo yung numbers sa ratio. 3+4+5 = 12
then gawin mong fraction yung number sa ratio.
3/12 : 4/12 : 5/12

cesar = 3/12 bert = 4/12 danny = 5/12
multiply mo na yung kay danny sa 24 para makuha yung hours ni danny.
5/12 * 24 = 10
then multiply 10 sa rate which is P50.
P500 po yung sagot :)

2. anu po number yan?

28. Y number is letter d? Dva the average of the 5 numbers is 20?

29. can you show computations/solutions please
thanks

30. Number 1. The answer is 140kph. Therefore: the answer is A.

1. Hi! I think you just added 60kph + 80kph, tama ba? That only works if the two vehicles left in OPPOSITE directions. :) For this problem, you need to find the HYPOTENUSE of the triangle formed by the two buses. The distance traveled by each bus represents the legs of the triangle. Applying the PYTHAGOREAN THEOREM, you get 100kph. That's basically just the square root of (60^2 + 80^2). ^_^

31. The answer in number 4 is 588. Please check this item. Thanks

1. Hello po sa # 4 hindi po ba ganito ang pag solve?
0.4(5x-1470)=x
0.4x5x=2x
0.4x1470=588
2x588=x
2x+x=3x
3x/3 =remove
588/3 =196
Tama po ba?

32. Hi how do you solve number 13? Thanks!

1. Ana = 1/5 of the job (3 hrs)
Beth = x (3hrs)
Ana and Beth = 1 job

1/5(3) + 3x = 1
3/5 + 3x = 1
3x = 1 - 3/5
3x = 2/5
x = 2/5 /3
x= 7.5

2. paano kinuha yung 7.5 nah sagut?? bakit x=2/5/3 bakit ang sagut is 7.5??? ano ang solution pls

3. 1/5 = ana
1/n = beth
1/3 = both

1/5 + 1/n = 1/3
1/n = 1/3 - 1/5
1/n = 5/15 - 3/15
1/n = 2/15
2n = 15
n = 15/2
n = 7 1/2

4. AnonymousJune 24, 2018

pano po if unknown si ana? then 7.5 si beth? pano po?

33. solution of number 7 please. thanks

1. solution for number 7

5x + 4x + 1x = 62000
10x = 62000
10 10
x = 6200

5(6200) = 31000
4(6200) = 24800
1(6200) = 6200

31000-6200 = 24000

34. sa number 21 po anu sagot?

1. #21. A retailer buys candies for P90.25. The pack has 35 pieces of candies. If she sells each candy for P2.25, how much profit does she make?
a. P11.50
b. P56.25
c. P37.50
d. P18.75

Profit = Sales - Cost of goods
Profit = (35*2.25) - 90.25
Profit = 78.75 - 90.25
Profit = (-) 11.50

It is a negative profit..so it's a loss.

35. Hi po mga maam and sir ano po solution ng number18?

1. #18 is a ratio and proportion just take note of the total population which is 180.
boys + girls = 180.

the ratio is
(boys) / (boys+girls) = 5 / (5+7)
5/12 of the entire population are boys = 75.

(girls) / (boys+girls) = 7 / (5+7)
7/12 of the entire population are girls = 105.

36. pa check naman ng number 3 ...thanks

37. AnonymousMay 11, 2018

how to download the reviewer from this?

38. paano po yung 25? tama po ba yung [(x1 + x2)/2, (y1 + y2)/2]? Thanks

1. AnonymousMay 31, 2018

iadd mo lang yung dalawang x values diveded by 2 para magkaroon ka ng x midpoint. same process sa y values para naman sa y midpoint

39. AnonymousJune 12, 2018

paano po yung solution sa number 9, i'm so confused po i really need help

40. AnonymousJune 13, 2018

yung item # 4, answer is D. Bakit po ganun, eh choices is up to C lang?

41. AnonymousJune 15, 2018

bakit po ganun yung 3? ^_^

42. AnonymousJune 24, 2018

How to solve item no.3 ?? plss

1. 3. Which of the following is the factorization of the binomial x^2 - 4^2?
a. (x + 4)(x + 2)
b. (x – 4)^2
c. x(x + 2x + 2)
d. (x – 4)(x + 4)

The binomial is in the form of (a^2 – b^2), a difference of two squares.
Difference of two squares can be factored as (a+b) (a-b)
Let
a = x
b = 4
So.. (a+b) (a-b) = (x+4) (x-4)

2. Ee diba po mafafactor mo pa yun 4 sa 2. Di po ba dapat (x-2)(x+2)?

43. in no. 21 why is it profit? suppose to be dba dapat lugi cya???

44. Wala po bang solutions?

45. opo walang solution?

46. nasaan po ang letter d sa no. 4?

47. Hindi po ba 140 yung sagot sa number 1? Dba po 30x2=60 then 40x2=80 2 dahil 2hrs na yung nakalipas tas 60+80=140?

1. paiwas po ang takbo nila mam... north ang isa.. west po yung isa forming a triangle kaya po pythagorean formula po

48. Anong tamang sagot sa nos. 14 and 21?

1. Answer to number 14 is B. 3,775

Using Gauss formula... the sum of 1 to n = n(n+1)/ 2

1 to 50 = 50(50+1)/2 = 1275
1 to 100 = 100(100+1)/2 = 5050
So, 5050 - 1275 = 3,775

49. Pano po ung series of number

50. solution for number 1 please

51. Paano po kinuha yung 1? hehe thank you :)

52. wala po sa choices yung sa number 4. Wala po yung letter D. thank you po