Answer Key: CSER β Solutions 2
2
111. 3 is to 9 as 9 is to __________ 1. 18 2. 27
3. 72
4. 81
5. 90
Solution: This is the safest and the correct way to answer. 32 92 9 (92 ) = ; π₯ = = 81 9 π₯ 32 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 canβt 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 92 9 (92 ) = ; π₯ = = 27 9 π₯ 32 Again, this answer could be possible if it is in a series problem. Logically, in a ratio and proportion problem, this is wrong.
112. 30% is to 3/5 as 60% is to __________ 1. 1 1/5 2. 1 ΒΌ 3. 3 Β½
4. 2 1/3
5. 2 ΒΎ
4. 1.125
5. 0.625
Solution: 30 3 5
60
=
π₯
;π₯=
60 (3 5) 30
=2 3 5 = 6 5=1 1 5
113. 0.25 is to 0.125 as 1.25 is to __________ 1. 6.250 2. 2.125 3. 1.625 Solution: 0.25 0.125
=
1.25 π₯
;π₯=
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.
114. 12.5 is to 1/8 as 20 is to __________ 1. 1/6 2. 1/5
3. ΒΌ
4. 1/3
5. Β½
4. 72
5. 60
Solution: 12.5 1 8
=
20 π₯
;π₯=
1/8 (20) 12.5
20
= 100 = 1/5
115. 6 is to 15 as 36 is to ___________ 1. 90 2. 82 Solution:
3. 75 6 15
=
36 π₯
;π₯=
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.
DIRECTION: Number Series 116.
9.12 1. 3.25
18.13
16.15 13.18 2 . 4.27
9.22 3. 5.23
__________ 4. 6.29
5. 5.26
Solution:
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.
117.
1 1. 623
4
13 2. 719
40
121 3. 865
364
__________ 4. 997
5. 1093
Solution:
1
4
13
3 3
9 3x3
40
27 9x3
121 81 27x3
364
243 81x3
______
____ 243x3
Taking the difference from each number in the series, youβll notice that the difference is also a series of 3 multiples. The answer should be 364 + (243x3) = 1093.
118.
5 1. 17
17
19 2. 15
6
14 3. 11
16
7 4. 9
10
12
8 5. 5
_________
Solution:
5
17
19 +1
6 -3
14 -3
16
+1
7 -4
10 -4
12
+1
8
_________
_____
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, youβll get the pattern. The number should be 10 β 5 = 5.
119.
795 1. 543
2611
684 2. 484
2722
573 3. 462
2833
__________ 4. 446
5. β426
Solution:
795
2611 -111
684 +111
2722 -111
573
2833
+111
-111
__________
In here, the series is in 2 parts or alternating, youβll know that these series are alternating because they are suspiciously longer than the regular series problem. Once you get the pattern, then youβll have the correct answer.
120.
-6 30 1. 3750
-150 750 2. 2250
__________ 3. β1500
4. β2250
5. β3750
Solution: -6
30
-6x-5
-150
750
_____
30x-5 -150x-5 750x-5
In here, this problem is a series of multiples of -5 of the first number.
121.
1/3 3/9 1. 11/35
5/15 7/21 2. 11/33
9/27 __________ 3. 9/29 4. 8/25
5. 4/13
Solution: 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.
122.
4 1. 480
16
8 2. 360
40
20 3. 240
120
60 4. 210
420
__________ 5. 140
Solution: 4
16 x4
Γ·2
8 x5
40 Γ·2
20 x6
120 Γ·2
x7
60 Γ·2
420
__________
Once you get the pattern, this problem would be very easy, you donβt have to worry about the other numbers in the series, and youβll just have to know that the last number would only be divided by 2 to get the next number.
NUMBER ANALOGY ANSWERS 1. 0.75 is to ΒΎ 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:
therefore the ratio 0.75 is to ΒΎ or
ππ. ππππ =
ππ.ππππ ππ/ππ
ππππ ππ Γ ππππ ππ Γ ππππ ππ = = = ππππππ ππ Γ ππππ ππ Γ ππππ ππ
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: ππ. ππππ =
Solution 2: Ratio and Proportion Convention
ππππ ππ Γ ππππ ππ Γ ππ ππ = = = ππππππ ππππ Γ ππππ ππ Γ ππ ππ
0.75 is to ΒΎ as 0.8 is to X, (X is unknown). ππ
0.75:ππ = 0.8:X ππ. ππππ ππ. ππ = ππ/ππ ππ
ππππ
Convert 0.75 and 0.8 to fraction form. (Review Fractions: 0.1 = ππππππ ππππ ππππ/ππππππ ππππ/ππππππ = ππ/ππ ππ ππππ
ππ
ππππππ(ππ)
=
ππππ ππππππ(ππ)
ππππ (ππ) ππππ = ππππππ(ππ) ππππππ(ππ)
ππππ(ππππππ)(ππ)
ππ = ππππππ(ππππ)(ππ) =
2. 75% is to 1/2 as 45% is to ________ 1. 3/11 2.3/10 3.3/4 4.2/3
ππππ(ππ)
= (ππππ)(ππ)
ππ =
ππ ππ
ππππ (ππ)(ππ) ππππ(ππ)(ππ)
=
ππ (ππ) ππ(ππ)
5. 3/5
Solution: Ratio and Proportion Convention 75% is to Β½ as 45% is to X, (X is unknown).
ππ
ππ
, 0.01 = ππππππ ) ππππ
ππ
75%:ππ = 45%:X ππππ% ππππ% = ππ ππ/ππ
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 ππππ/ππππππ ππππ/ππππππ = ππ/ππ ππ
ππππ ππππ = ππππππ(ππ/ππ) ππππππ(ππ) ππππ (ππ) ππππ = ππππππ(ππ) ππππππ(ππ)
ππππ(ππππππ)(ππ)
ππ = ππππππ(ππππ)(ππ) =
3. 0.25 is to 0.125 as to 1.25 is to ________ 1. 0.625 2. 1.125 3. 1.625
ππππ
(ππππ)(ππ)
ππ =
ππ (ππ)
ππ (ππ)
= ππ(ππππ)(ππ) = ππ(ππ)(ππ)
ππ ππππ
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
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
4.4/6
5. 5/6
5. 15
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
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. Β½
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 ΒΎ 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 β 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
1.09
6.36
1.11
7.49
1.13
8.64
_______________.
1.15 (1.17)
The answer should be 8.64 + 1.17 = 9.81 1. 9.36 2. 9.81 2. 5
6
3. 8.81 4. 6.64 10
19
35
5. 7.72 60
______________.
Answer: Taking/comparing the difference of each number from its predecessor, youβll notice that the difference is of special property. They are all squares of a number. 5
6 1 12
10 4 22
19 9 32
35 16 42
60 25 52
______________. 36 62
The answer should be 60+36=96. 1. 98 2. 86 3. 4/3-2/3
3. 96 4. 72 -1/3
1/6
5. 36 -1/12
-1/18 ___________.
Answer: Just divide the number by 2 and alternate the +/- signs one + and two β or +, -, -, +, -, -, +β¦ 4/3 Γ· 2 = 2/3 2/3 Γ· 2 = 1/3 1/3 Γ· 2 = 1/6 1/6 Γ· 2 = 1/12 1/12 Γ· 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 Γ· 2 = 1/36 The true answer should be 1/48.. 1. 4/3 2. 2/3 4. .25 1 1. 10.25 2. 12.25
3. 1/36 4. 1/3 5.25 3. 15.75 4. 13.25
5. β3/4 6 _____________ 5. none
