Answer Key: CSER – Solutions 111. 32 is to 9 as 92 is to __________ 1. 18 2. 27 3. 72 4. 81 5. 90 Solution: This is the safest and the correct way to answer.

112. 30% is to 3/5 as 60% is to __________ 1. 1 1/5 2. 1 ¼ 3. 3 ½ 4. 2 1/3 5. 2 ¾ Solution:

113. 0.25 is to 0.125 as 1.25 is to __________ 1. 6.250 2. 2.125 3. 1.625 4. 1.125 5. 0.625 Solution:

114. 12.5 is to 1/8 as 20 is to __________ 1. 1/6 2. 1/5 3. ¼ 4. 1/3 5. ½ Solution:

115. 6 is to 15 as 36 is to ___________ 1. 90 2. 82 3. 75 4. 72 5. 60 Solution:

DIRECTION: Number Series 116. 9.12 18.13 16.15 13.18 9.22 __________ 1. 3.25 2 . 4.27 3. 5.23 4. 6.29 5. 5.26 Solution:

117. 1 4 13 40 121 364 __________ 1. 623 2. 719 3. 865 4. 997 5. 1093

9.12 18.13 16.15 13.18 9.22 _______

+9.+1 -2.+2 -3.+3 -4.+4 (____) Study the series, how it runs, how it progresses. In here, you can notice that the whole number is reducing while the decimal is gaining. Try getting the difference of each number. Notice that the first number is wrongly typed (clerical error), it should have been 19.12 for the series to be consistent. However, we can just ignore the first number. From the difference comparison, we can say that the 6th number should be (9-5), (22+5) or 4.27.

6

15=

36

𝑥 ; 𝑥 =

36 (15)

6= 6(15) = 90

In here, you can observe the relationship between the 1st and the 3rd number, which is 36 is 6x6, applying the relationship to the 2nd number, we 15 x 6=90.

12.51

8 =

20

𝑥 ; 𝑥 =

1/8 (20)

12.5=

20

100= 1/5

0.25

0.125=

1.25

𝑥 ; 𝑥 =

1.25 (0.125)

0.25=

1.25

2= 0.625

You can also try observing the relationship of the first ratio. Say 0.25 to 0.125 is just 0.25 divided by 2 = 0.125, so you should divide the third number by 2, 1.25 divided by 2 = 0.625, which is just the same with the solution above.

303

5 =

60

𝑥 ; 𝑥 =

60 (35 )

30= 2 3

5 = 65 = 1 1

5

32

9=

92

𝑥 ; 𝑥 =

9 (92)

32 = 81 In the answer key, the correct answer is 27, which can also be correct if there are more given numbers, or if the problem is in series. I can’t verify if this is an actual exam or if it is the official answer keys, if it is then, if you meet this problem in the exam, you should answer 27. Why 27?

32

9=

92

𝑥 ; 𝑥 =

9 (92)

32 = 27 Again, this answer could be possible if it is in a series problem. Logically, in a ratio and proportion problem, this is wrong.

Solution:

118. 5 17 19 6 14 16 7 10 12 8 _________ 1. 17 2. 15 3. 11 4. 9 5. 5 Solution:

119. 795 2611 684 2722 573 2833 __________ 1. 543 2. 484 3. 462 4. 446 5. –426 Solution:

120. -6 30 -150 750 __________ 1. 3750 2. 2250 3. –1500 4. –2250 5. –3750 Solution:

121. 1/3 3/9 5/15 7/21 9/27 __________ 1. 11/35 2. 11/33 3. 9/29 4. 8/25 5. 4/13 Solution:

122. 4 16 8 40 20 120 60 420 __________ 1. 480 2. 360 3. 240 4. 210 5. 140 Solution:

4 16 8 40 20 120 60 420 __________ x4 ÷2 x5 ÷2 x6 ÷2 x7 ÷2 Once you get the pattern, this problem would be very easy, you don’t have to worry about the other numbers in the series, and you’ll just have to know that the last number would only be divided by 2 to get the next number.

1/3 3/9 5/15 7/21 9/27 ______ +2/+6 +2/+6 +2/+6 +2/+6 +2/+6 This series is like 2 series grouped into a fraction. The numerator is a series and the denominator is another series. Just like in problem 116, in which the whole numbers and the decimals are in different series. This is just to confuse the examinees who have only met this kind of problem. After knowing the pattern, which is +2/+6, the answer should be 9+2/27+6 or 11/33.

-6 30 -150 750 _____ -6x-5 30x-5 -150x-5 750x-5 In here, this problem is a series of multiples of -5 of the first number.

795 2611 684 2722 573 2833 __________

-111 +111 -111 +111 -111 In here, the series is in 2 parts or alternating, you’ll know that these series are alternating because they are suspiciously longer than the regular series problem. Once you get the pattern, then you’ll have the correct answer.

5 17 19 6 14 16 7 10 12 8 _________

+1 -3 -3 +1 -4 -4 +1 _____ Notice that the series is quite long for a series. It means that the series may be in group. At first, I studied the series, which would bring a pattern because the 1st, 2nd and 3rd does not make sense, then I noticed that there is 5, 6, 7 and 8 in the series, it could be the breakpoints of the group. Taking the difference of number to the next third number, you’ll get the pattern. The number should be 10 – 5 = 5.

1 4 13 40 121 364 ______

3 9 27 81 243 ____

3 3x3 9x3 27x3 81x3 243x3 Taking the difference from each number in the series, you’ll notice that the difference is also a series of 3 multiples. The answer should be 364 + (243x3) = 1093.

NUMBER ANALOGY ANSWERS 1. 0.75 is to ¾ as 0.8 is to _________

1. 2/3 2.4/5 3.5/6 4.6/7 5. 3/5 Solution 1: Comparison If you convert 0.75 into fraction form:

𝟎𝟎.𝟕𝟕𝟕𝟕 =𝟕𝟕𝟕𝟕𝟏𝟏𝟎𝟎𝟎𝟎

=𝟑𝟑 × 𝟐𝟐𝟕𝟕𝟒𝟒 × 𝟐𝟐𝟕𝟕

= 𝟑𝟑 × 𝟐𝟐𝟕𝟕𝟒𝟒 × 𝟐𝟐𝟕𝟕

=𝟑𝟑𝟒𝟒

therefore the ratio 0.75 is to ¾ or 𝟎𝟎.𝟕𝟕𝟕𝟕𝟑𝟑/𝟒𝟒

is equal to one. Since the first ratio is equal (0.75=3/4), you only need to

find the fraction form that would equal to 0.80:

𝟎𝟎.𝟖𝟖𝟎𝟎 = 𝟖𝟖𝟎𝟎𝟏𝟏𝟎𝟎𝟎𝟎

=𝟖𝟖 × 𝟏𝟏𝟎𝟎𝟏𝟏𝟎𝟎 × 𝟏𝟏𝟎𝟎

=𝟒𝟒 × 𝟐𝟐𝟕𝟕 × 𝟐𝟐

=𝟒𝟒𝟕𝟕

Solution 2: Ratio and Proportion Convention

0.75 is to ¾ as 0.8 is to X, (X is unknown).

0.75:𝟑𝟑𝟒𝟒 = 0.8:X

𝟎𝟎.𝟕𝟕𝟕𝟕𝟑𝟑/𝟒𝟒

=𝟎𝟎.𝟖𝟖𝐗𝐗

Convert 0.75 and 0.8 to fraction form. (Review Fractions: 0.1 = 𝟏𝟏𝟎𝟎𝟏𝟏𝟎𝟎𝟎𝟎

𝒐𝒐𝒐𝒐 𝟏𝟏𝟏𝟏𝟎𝟎

, 0.01 = 𝟏𝟏𝟏𝟏𝟎𝟎𝟎𝟎

)

𝟕𝟕𝟕𝟕/𝟏𝟏𝟎𝟎𝟎𝟎𝟑𝟑/𝟒𝟒

=𝟖𝟖𝟎𝟎/𝟏𝟏𝟎𝟎𝟎𝟎

𝐗𝐗

𝟕𝟕𝟕𝟕

𝟏𝟏𝟎𝟎𝟎𝟎(𝟑𝟑𝟒𝟒)

=𝟖𝟖𝟎𝟎

𝟏𝟏𝟎𝟎𝟎𝟎(𝐗𝐗)

𝟕𝟕𝟕𝟕 (𝟒𝟒)𝟏𝟏𝟎𝟎𝟎𝟎(𝟑𝟑)

=𝟖𝟖𝟎𝟎

𝟏𝟏𝟎𝟎𝟎𝟎(𝐗𝐗)

𝐗𝐗 = 𝟖𝟖𝟎𝟎(𝟏𝟏𝟎𝟎𝟎𝟎)(𝟑𝟑)𝟏𝟏𝟎𝟎𝟎𝟎(𝟕𝟕𝟕𝟕)(𝟒𝟒)

= 𝟖𝟖𝟎𝟎(𝟑𝟑)(𝟕𝟕𝟕𝟕)(𝟒𝟒)

= 𝟐𝟐𝟎𝟎 (𝟒𝟒)(𝟑𝟑)𝟐𝟐𝟕𝟕(𝟑𝟑)(𝟒𝟒)

= 𝟒𝟒 (𝟕𝟕)𝟕𝟕(𝟕𝟕)

𝐗𝐗 =𝟒𝟒𝟕𝟕

2. 75% is to 1/2 as 45% is to ________

1. 3/11 2.3/10 3.3/4 4.2/3 5. 3/5

Solution: Ratio and Proportion Convention

75% is to ½ as 45% is to X, (X is unknown).

75%:𝟏𝟏𝟐𝟐 = 45%:X

𝟕𝟕𝟕𝟕%𝟏𝟏/𝟐𝟐

=𝟒𝟒𝟕𝟕%𝐗𝐗

Convert 75% and 80% to fraction form. (Review: Percentage is a way of expressing a number as a fraction of 100 (per cent meaning "per hundred" in Latin) 75% = 75/100, 80% = 80/100 like any number with a % sign like 0.01% = .01/100 and 2000% = 2000/100

𝟕𝟕𝟕𝟕/𝟏𝟏𝟎𝟎𝟎𝟎𝟏𝟏/𝟐𝟐

=𝟒𝟒𝟕𝟕/𝟏𝟏𝟎𝟎𝟎𝟎

𝐗𝐗

𝟕𝟕𝟕𝟕

𝟏𝟏𝟎𝟎𝟎𝟎(𝟏𝟏/𝟐𝟐)=

𝟒𝟒𝟕𝟕𝟏𝟏𝟎𝟎𝟎𝟎(𝐗𝐗)

𝟕𝟕𝟕𝟕 (𝟐𝟐)𝟏𝟏𝟎𝟎𝟎𝟎(𝟏𝟏)

=𝟒𝟒𝟕𝟕

𝟏𝟏𝟎𝟎𝟎𝟎(𝐗𝐗)

𝐗𝐗 = 𝟒𝟒𝟕𝟕(𝟏𝟏𝟎𝟎𝟎𝟎)(𝟏𝟏)𝟏𝟏𝟎𝟎𝟎𝟎(𝟕𝟕𝟕𝟕)(𝟐𝟐)

= 𝟒𝟒𝟕𝟕(𝟕𝟕𝟕𝟕)(𝟐𝟐)

= 𝟕𝟕 (𝟗𝟗)𝟕𝟕(𝟏𝟏𝟕𝟕)(𝟐𝟐)

= 𝟑𝟑 (𝟑𝟑)𝟕𝟕(𝟑𝟑)(𝟐𝟐)

𝐗𝐗 =𝟑𝟑𝟏𝟏𝟎𝟎

3. 0.25 is to 0.125 as to 1.25 is to ________ 1. 0.625 2. 1.125 3. 1.625 4. 2.125 5. 6.250

Try Solving This:

Solution 1: By Comparison Solution 2: By Ratio and Proportion Convention

4. 2 is to 50 as 3.2 is to _________

1. 60 2. 70 3.80 4.90 5. 160 Try Solving This by Ratio and Proportion Convention

5. 14 is to 28 as 5 is to _________ 1. 7 2. 8 3.9 4.10 5. 15

6. 1 is to 1/4 as 5/25 is to ________

1. 1/16 2.1/18 3.2/6 4.3/4 5. 1/20

7. 0.35 is to 7 as 0.45 is to ________ 1. 8 2.9 3.12 4.14 5. 0.9

8. 1/3 is to 2/18 as 1/12 is to ________

1. 2/72 2. 2/48 3.3/36 4.3/25 5. 1/72

9. 3/8 is to 12/32 as 2/5 is to ________ 1. 8/20 2. 10/23 3.6/13 4.4/6 5. 5/6

10. 1/3 is to 3/7 as 1/6 is to ________

1. 3/14 2. 1/5 3.1/4 4.1/3 5. ½

11. 0.4 is to 2/5 as 0.6 is to ________ 1. 20 2. 4/5 3.3/10 4.3/5 5. 1/5

12. 0.2 is to 0.4 as 0.3 is to ________

1. 0.009 2. 0.0009 3.0.09 4. 0.9 5. 9.0

13. 8 is to 23 as 27 is to ________ 1. 33 2. 53 3.93 4.39 5. 43

14. 0.5 is to 1/2 as 0.65 is to ________

1. 11/20 2.13/20 3.15/20 4.17/20 5. 14/20

15. 1/3 is to 3 as 2/8 is to ________ 1. 2 2.4 3.6 4.8 5. 10

16. 30% is to 3/5 as 80% is to ________

1. 1 1/5 2.1 2/5 3.1 3/5 4.1 4/5 5. 2

17. 0.30 is to 0.075 as 0.15 is to ______ 1. 0.000375 2. 0.00375 3.0.0375 4.0.375 5.none

18. 2/5 is to 20% as ¾ is to ________

1. 35.5% 2. 37.0% 3. 37.5% 4. 39.0% 5. 36.5%

19. 625 is to 81 as 5 is to ________ 1. 3 2. 4 3.6 4.9 5. 0.648

Note: Solution is by comparison. The ratio here is exponential: 54:34, after knowing this the answer is obvious. It is 3. Review special numbers like the squares of number. My first analysis here is that it is 252 and 92 and I know that 25 and 9 are52 and 32 which made me arrive to the same answer 3.

20. 8 is to 11 as 36 is to ________

1. 49.50 2. 55.00 3. 59.50 4. 65.00 5. 69.50

21. 2 is to 2.5 as 4 is to ________ 1. 3 2.5 3.7 4.9 5. 6

22. 2 is to 8 as 4 is to ________

1. 18 2. 32 3.36 4.66 5.none

NUMBER SERIES

1. 4.16 5.25 6.36 7.49 8.64 _______________.

Answer: Taking/comparing the difference of each number from its predecessor.. (minuend − subtrahend =difference) Take note of their progression: each difference is .02 higher than its predessor. The next number of the series should have 1.17 or 1.15+0.02 difference from the last number.

4.16 5.25 6.36 7.49 8.64 _______________.

1.09 1.11 1.13 1.15 (1.17)

The answer should be 8.64 + 1.17 = 9.81

1. 9.36 3. 8.81 5. 7.722. 9.81 4. 6.64

2. 5 6 10 19 35 60 ______________.

Answer: Taking/comparing the difference of each number from its predecessor, you’ll notice that the difference is of special property. They are all squares of a number.

5 6 10 19 35 60 ______________.

1 4 9 16 25 36 12 22 32 42 52 62

The answer should be 60+36=96.

1. 98 3. 96 5. 36 2. 86 4. 72

3. 4/3-2/3 -1/3 1/6 -1/12 -1/18 ___________.

Answer: Just divide the number by 2 and alternate the +/- signs one + and two – or +, -, -, +, -, -, +…

4/3 ÷ 2 = 2/32/3 ÷ 2 = 1/31/3 ÷ 2 = 1/61/6 ÷ 2 = 1/121/12 ÷ 2 = 1/24 -> OOPS!! This must be a clerical error on the examiner part but do not

let it distract you.. Assume that the answer is 1/18..1/18 ÷ 2 = 1/36The true answer should be 1/48..

1. 4/3 3. 1/36 5. –3/4 2. 2/3 4. 1/3

4. .25 1 5.25 6 _____________ 1. 10.25 3. 15.75 5. none 2. 12.25 4. 13.25