2. The sum of three different three digits is 2993, so these three addends are _ _ _ _ _.

3. When calculating division with remainder, Xiao Ming mistook dividend 472 for 427, and the result quotient was 5 smaller than the original, but the remainder was exactly the same. Then the rest of the question is _ _ _ _.

4. The number of all two-digit numbers with exactly four divisors in a natural number is _ _ _ _ _.

5. As shown in the figure, it is known that the area of each small square cell is 1 cm2, so the area of the irregular figure is _ _ _ _ _.

6. The existing 2 grams, 3 grams and 6 grams each have a weight, so you can weigh _ _ _ _ kinds of objects with different weights on the balance.

7. There is a formula:

Approximation of five, then the numbers in formula □ are _ _ _ _ _ _.

8. A job will be completed by Party A alone for 45 days, and then by Party B alone 18 days. If both parties cooperate, it can be completed in 30 days. Now it takes _ _ _ _ _ days for Party A to do it alone for 20 days, and then Party B does it alone.

9. A factory fleet has three vehicles to organize the circular transportation of five workshops A, B, C, D and E. As shown in the figure, the number marked is the number of stevedores required in each workshop. In order to save manpower, some stevedores should follow the car, and at least _ _ _ _ stevedores should be arranged to ensure the needs of each workshop.

10. There are 340 grams of pure alcohol in container A and 400 grams of water in container B. Pour part of pure alcohol in container A into container B for the first time to mix alcohol with water. Pour part of the mixed liquid in container B into container A for the second time. At this time, the pure alcohol content in container A is 70%, and the pure alcohol content in container B is 20%, so the mixed liquid poured from container B into container A for the second time is _ _ _ _ _ _ _ _ _.

Second, answer questions:

1. There are a bunch of red and yellow glass balls, of which the number of red balls is 1.5 times that of yellow balls. If you take out five red balls and four yellow balls from this pile at the same time, how many times will there be nine red balls and two yellow balls left?

2. The total age of four people in Xiaoming's family is 147 years old. Grandpa is 38 years older than his father and his mother is 27 years older than Xiaoming. Grandpa's age is twice that of Xiaoming and his mother combined. How old are the four Xiaoming family members?

3. Five people, A, B, C, D and E, got 94 points in an exam, out of 100. B was the first, C was the average score of A and D, D was the average score of five people, and E was the second. How many points did B get?

4. Party A and Party B run around the circular track at a uniform speed, starting at both ends of the circular diameter. If they start at the same time and meet for the first time when Party A runs 60 meters, and meet for the second time when Party B runs 80 meters less, what is the length of the track? Answer:

First, fill in the blanks:

1.648

The original formula = 7.2× 61.3+(61.3+12.5 )× 2.8 = (7.2+2.8 )× 61.3+12.5.

=6 13+35

=648

Since 1993 ÷ 3 = 997...2, these three addends must be close to 997. Obviously, the sum of 997, 998 and 998 is 2993. But because the three addends are different, it should be 996,998,999 after adjustment.

3.4

In these two division calculations, the divisor and remainder remain the same, but the quotient is smaller than the original. 5. Let the divisor be a and the remainder be r, then

472=a× quotient +r

427=a× (quotient -5)+r

There are 472-427=a×5, and a=(472-427)÷5=9.

472÷9=52…4

So the remainder r = 4.

4.30

Because 4= 1×4=2×2, a number with four divisors must be expressed as a3 or ab, and A and B are prime numbers.

For a3, only when a=3, a3=27 is a two-digit number, that is, 1 number satisfies the condition.

For ab, when a=2, B = 5,7, 1 1, 13, 17,19,23,29,31,37,4. When a=3 and b is a prime number greater than 3 and less than 37, there are 9 that meet the conditions; Similarly, when a=5, there are five; There are two when a=7. Then the number of all the two digits in a natural number with exactly four divisors is:

1+ 13+9+5+2 = 30 (pieces)

5. 19 cm2

The figure is irregular, so it is easy to find the area of the figure marked 1, 2, 3, 4, 5, 6, 7 by division. Subtract the area of these seven figures from the whole rectangular area to get the figure, so the area of the irregular figure is:

8×6-3×2÷2×3-( 1+3)×3÷2-2×4÷2-(2+4)× 1÷2-(3+4)×2÷2

=( 19 cm2)

6. 10

There is no limit that weights can only be placed on the same scale of the balance, so weights can be placed on the scales on both sides of the balance. Although the weight is only two grams, three grams and six grams, if one side of the balance is two grams and the other side is three grams, an object with a weight of 1 gram can be weighed. If you put them on the same side, you can weigh an object weighing 5 grams. Similarly, weights of two grams and six grams can be called four grams or eight grams. 3 g and 6 g weights can weigh 3 g or 9 g objects, of which 3 g weights can be directly weighed; Objects weighing 7 g, 5 g, 1 g, 1 1 g can be weighed by 2 g, 3 g and 6 g; So these three weights can be used to weigh 1, 2, 3, 4, 5, 6, 7, 8, 9, 1 1g * * 10 objects with different weights.

7. 1,3,3

So there are150.15 ≤ 55×□+22×□+10×□≤151.14.

Because the number in □ is an integer, so

55×□+22×□+ 10×□= 15 1

Only 55×1+22× 3+10× 3 =151

So the numbers in □ are filled in 1, 3, 3 in turn.

8.38

According to the meaning of the question, both parties can finish the work within 30 days. Party A can do it for 45 days, 15 days is more than 30 days, and Party B can do it less.

30- 18= 12 (days)

Explain that the price of a 15 days is equal to that of b 12 days.

Now Party A works 20 days, less than 30 days 10 days. How many days does it take Party B to complete 10?

B also need to do it alone:

30+8=38 (days)

9.2 1

3 stevedores will be dispatched from each workshop, and 3×5= 15 people will be dispatched from * *, with 3 people per vehicle. * * 3 = 9 people are needed, which can save 15-9=6 (people). At this time, there are 3 people in A, 2 people in B, 4 people in C and 0 people in D..

5×3+ 1+2+3=2 1 (person)

Pour a part from container B into container A for the second time without changing the alcohol concentration in container B, so the alcohol concentration in container B is obtained by pouring a part of pure alcohol into container A for the first time, so the ratio of alcohol to water in container B is:

20%∶( 1-20%)= 1∶4

Then pour 100g from container A to container B for the first time, and the ratio of pure alcohol to water in container B is exactly:

100∶400= 1∶4

After the second pouring, the ratio of alcohol to water in container A is as follows

70%∶( 1-70%)=7∶3

Suppose that X grams of alcohol solution is poured out of container B for the second time, then there will be pure wine in container A after the second pouring.

So the mixed solution poured from container B to container A for the second time is144g.

Second, answer questions:

1. I took it 6 times, and there are 9 red balls and 2 yellow balls left.

After x times, there are 9 red balls and 2 yellow balls left.

5x+9=(4x+2)× 1.5

5x+9=6x+3

x=6

So after six times, there are nine red balls and two yellow balls left.

Xiaoming is 5 years old, his mother is 32 years old, his father is 36 years old and his grandfather is 74 years old.

The sum of the ages of mom and Xiaoming:

(147+38) ÷ (2× 2+1) = 37 (years old)

Xiao Ming's age: (37-27)÷2=5 (years old)

Mother's age: 37-5=32 (years)

Grandpa's age: 37×2=74 years old.

Dad's age: 74-38=36 (years old)

3.b got 98 points.

The score of D is the average score of five people, and D is higher than A, otherwise D will be the lowest score of five people, so it can't be the average score of five people. The scores of five people from high to low are B, E, D, C and A respectively.

The score from C is the average score of A and D. Because A is 94 and 94 is even, D should be even, but D won't get 100, otherwise B will get 100. D=98, then C=96, E=98, B = 98× 5-(98+96+94+98) =104, which cannot exceed 100; So D=96, C=95, E=97, and b is.

96× 5-(97+96+95+94) = 98 (minutes)

The length of the runway is 200 meters.

When we first met, A and B * * * ran half a lap, of which A ran 60 meters. Let's assume that the length of the half track is x meters, and B ran x-60 meters at the first meeting. From the start to the second meeting between A and B, * * * ran three and a half laps. Because they run at a constant speed, B should run three and a half laps and three (x-60) meters, but

3(x-60)=2x-80

3x- 180=2x-80

x= 100

2x = 2x100 = 200 (m)

So the length of the circular runway is 200 meters.