Problem and Solution SEAMO 2017 paper C

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9. \(< 6 >\) denotes the smallest whole number that is not a factor of 6.
For example, \(< 7 > = 2, < 12 > = 5\).
Find the value of

\(< < 23 > × < 100 > >\)

(A) 4
(B) 5
(C) 6
(D) 8
(E) 10

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Solution

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10. When a 6-digit number \(\overline{abcdef}\) is multiplied by 3, the result is \(\overline{bcdef9}\).

Find the value of \(\overline{abcdef}\).
(A) 286713
(B) 284713
(C) 297813
(D) 279813
(E) None of the above

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Solution

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11. Find the remainder when the 2017th term of the following sequence is divided by 5.

\(1, 2, 4, 7, 11, 16, 22, 29 …\)

(A) 1
(B) 2
(C) 3
(D) 4
(E) 0

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Solution

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12. All digits are different in the electronic clock display below.

How many times between 7:00:00 to 8:00:00 will all digits be different?
(A) 1242
(B) 1248
(C) 1254
(D) 1260
(E) None of the above

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Solution

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13. How many numbers are the same in both number patterns below?

\(1 , 3, 5 , 7 , 9 ,… , 2015 , 2017\)
\(1 , 4 , 7 , 10 ,… , 2014 ,2017\)

(A) 337
(B) 338
(C) 339
(D) 340
(E) None of the above

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Solution

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14. The figure shows a semicircle and a sector overlapping each other. Find the
perimeter of the shaded region. Take \(π =\frac{22}{7}\)

(A) \(43\)
(B) \(43\frac{1}{3}\)
(C) \(43\frac{2}{3}\)
(D) \(44\)
(E) None of the above

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Solution

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15. A camera was priced at 35% more than its original price and later sold at a 10% discount. The buyer also redeemed a $50 cash voucher. The net profit from the sale was $380. Find the original price of the camera.
(A) $1872
(B) $1900
(C) $2000
(D) $2172
(E) None of the above

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Solution

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16. Find the largest and smallest fraction in

\(\frac{9}{5}, \frac{12}{7}, \frac{27}{17}, \frac{36}{19}, \frac{54}{29}\)

(A) \(\frac{54}{29},\frac{9}{5}\)
(B) \(\frac{12}{7},\frac{27}{17}\)
(C) \(\frac{36}{19},\frac{54}{29}\)
(D) \(\frac{12}{7},\frac{27}{17}\)
(E) \(\frac{36}{19},\frac{27}{17}\)

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Solution

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17. Alan and Ben are working on a science project. Together, they can finish it in 35 days. If Alan works alone for 40 days, Ben will take a further 28 days to complete the project. If Alan works alone for 30 days, how many more days will Ben take to complete the project?
(A) 40
(B) 42
(C) 38
(D) 44
(E) None of the above

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Solution

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18. Evaluate

\((\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+…+\frac{1}{2017})(1+\frac{1}{2}+\frac{1}{3}+…+\frac{1}{2016})-(1+\frac{1}{2}+\frac{1}{3}+…+\frac{1}{2017})(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+…+\frac{1}{2016})\)

 

(A) \(\frac{1}{2015}\)
(B) \(\frac{1}{2016}\)
(C) \(\frac{1}{2017}\)
(D) \(\frac{1}{2013}\)
(E) None of the above

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Solution

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