Number puzzles – 1

Number puzzles

 

1. 1，6，19，63，(  )

A. 208

B. 210

C. 204

D. 209

Correct Answer: A. 208

Notes:

A(n+1)=A(n+2)X3+An

 

2. 2，1，4，4，8，9，16，(  )

A. 25

B. 36

C. 20

D. 16

Correct Answer: D. 16

Notes:

The odd-numbered terms are geometric progressions, and the even-numbered terms are square progressions.

 

3. 0, 3/2, 15/4, 35/6 (  )

A. 63/8

B. 3/2

C. 6

D. 15/2

Correct Answer: A. 63/8

Notes:

The denominator is an arithmetic progression, and the numerator can be decomposed into 0×1, 1×3, 3×5, 5×7, 7×9

 

4. 0，3，8，15，26，(  )

A. 19

B. 21

C. 30

D. 39

Correct Answer: D. 39

 

5. In a club, it is found that there are 8 students from the English Department and 9 students from the Physics Department. The number of members from the English Department in the club is at least the number of members from the Foreign Languages ​​College, and the number of members from the Foreign Languages ​​College is more than the total number of members in the club. Then the number of members in the club is (  ).

A. 18

B. 19

C. 20

D. 21

Correct Answer: B. 19

Notes:

The problem can be simplified as follows: Let the total number of members in the club be N, and the number of members from the Foreign Languages ​​College in the club be n, then we can get: n+9≤N …………… ③ From ①, we get: n≤10, and combined with ②, we get: ……………
④, ②, ③ combined, we get: ……………⑤, from ④, ⑤, we get: 18

 

6. In the laboratory, beakers A and B contain 300 grams of 13% and 700 grams of 7% hydrochloric acid solutions, respectively.
In order to teach students about hydrochloric acid, a teacher used two test tubes to take out equal amounts of solution from beakers A and B, respectively.
But because there was no mark, after the teaching was completed, he poured the hydrochloric acid solution from beaker A into beaker B, and the hydrochloric acid solution from beaker B into beaker A. Afterwards, it was measured that the concentration of hydrochloric acid in beakers A and B was the same. Then the amount of hydrochloric acid taken out from the two beakers was
(  ) grams.

A. 126

B. 210

C. 378

D. 525

Correct Answer: B. 210

Notes:

The salt content of hydrochloric acid A and B is 300×13%=39 and 700×7%=49 respectively, so the total amount of hydrochloric acid is 39+49=
88. Since the concentrations of A and B are the same in the end, the concentrations of A and B solutions are both 8.8%. Then the cross method is used to find that the ratio of 13% and 7% solutions in A solution is 3:7.

 

7. A and B work together to translate a foreign language textbook. After working together for 48 days, they receive another urgent translation task and one of them must transfer to that task. It is known that if A stays, he will need 20 days to complete the task, while if B stays, it will take 30 days to complete the task. It takes (  ) days for A to translate the book alone.

A. 75

B. 100

C. 150

D. 180

Correct Answer: B. 100

Notes:

From the last condition – the remaining work can be completed by A in 20 days and by B in 30 days, we know that the speed ratio of A and B is 3:2. Therefore, the work that B does in 48 days only takes A (48×2)/3=32 days, so it takes A 48+32+20=100 days to complete it alone.

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