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SAT problem solving explanation

Вопрос id:1931416
Of the following, which is greater than ½ ? 
?) 4/7
?) 2/5
?) 6/13
?) 4/9
?) 5/11
Вопрос id:1931417
If an object travels at five feet per second, how many feet does it travel in one hour?
?) 720
?) 300
?) 1800
?) 18000
?) 30
Вопрос id:1931418
What is the average (arithmetic mean) of all the multiples of ten from 10 to 190 inclusive?
?) 90
?) 105
?) 100
?) 110
?) 95
Вопрос id:1931419
A cubical block of metal weighs 6 pounds. How much will another cube of the same metal weigh if its sides are twice as long?
?) 12
?) 18
?) 48
?) 32
?) 24
Вопрос id:1931420
In a class of 78 students 41 are taking French, 22 are taking German. Of the students taking French or German, 9 are taking both courses. How many students are not enrolled in either course?
?) 54
?) 15
?) 24
?) 33
?) 6
Вопрос id:1931421
If f(x) = │(x² - 50)│, what is the value of f(-5) ?
?) 25
?) 0
?) -75
?) 75
?) -25
Вопрос id:1931422
( √2 - √3 )² =
?) 1
?) 5 - √6
?) 5 - 2√6
?) 1 - √2
?) 1 - 2√6
Вопрос id:1931423
230 + 230 + 230 + 230 =
?) 230
?) 8120
?) 232
?) 226
?) 830
Вопрос id:1931424
Amy has to visit towns B and C in any order. The roads connecting these towns with her home are shown on the diagram. How many different routes can she take starting from A and returning to A, going through both B and C (but not more than once through each) and not travelling any road twice on the same trip?
?) 6
?) 2
?) 4
?) 10
?) 8
Вопрос id:1931425
  In the figure above AD = 4, AB = 3 and CD = 9. What is the area of triangle AEC ?
?) 9
?) 13.5
?) 4.5
?) 18
?) 3
Вопрос id:1931426
Which of the following could be a value of x, in the diagram above?

?) 20
?) 50
?) any of the above
?) 10
?) 40
Вопрос id:1931427
Helpers are needed to prepare for the fete. Each helper can make either 2 large cakes per hour, or 35 small cakes per hour. The kitchen is available for 3 hours and 20 large cakes and 700 small cakes are needed. How many helpers are required?
?) 25
?) 15
?) 30
?) 20
?) 10
Вопрос id:1931428
Jo's collection contains US, Indian and British stamps. If the ratio of US to Indian stamps is 5 to 2 and the ratio of Indian to British stamps is 5 to 1, what is the ratio of US to British stamps?
?) 10 : 5
?) 20 : 2
?) 25 : 2
?) 5 : 1
?) 15 : 2
Вопрос id:1931429
A 3 by 4 rectangle is inscribed in circle. What is the circumference of the circle
?) 4π
?) 3π
?) 2.5π
?) 5π
?) 10π
Вопрос id:1931430
Two sets of 4 consecutive positive integers have exactly one integer in common. The sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set?
?) it cannot be determined from the information given
?) 8
?) 7
?) 4
?) 12
Вопрос id:1931431
If f(x) = (x + 2) / (x-2) for all integers except x=2, which of the following has the greatest value?
?) f(1)
?) f(0)
?) f(4)
?) f(3)
?) f(-1)
Вопрос id:1931432
  ABCD is a square of side 3, and E and F are the mid points of sides AB and BC respectively. What is the area of the quadrilateral EBFD ?
 
?) 6
?) 3
?) 4
?) 2.25
?) 4.5
Вопрос id:1931433
If n ≠ 0, which of the following must be greater than n?
I 2n
II n²
III 2 - n
?) II and III only
?) I only
?) I and II only
?) None
?) II only
Вопрос id:1931434
After being dropped a certain ball always bounces back to 2/5 of the height of its previous bounce. After the first bounce it reaches a height of 125 inches. How high (in inches) will it reach after its fourth bounce?
?) 3.2
?) 15
?) 20
?) 5
?) 8
Вопрос id:1931435
n and p are integers greater than 1
5n is the square of a number
75np is the cube of a number.
The smallest value for n + p is
?) 50
?) 30
?) 14
?) 20
?) 18
Вопрос id:1931436
Six years ago Anita was P times as old as Ben was. If Anita is now 17 years old, how old is Ben now in terms of P ?
?) 17/P
?) P/11 +6
?) 17 - P/6
?) 11.5P
?) 11/P + 6
Вопрос id:1931437
12 litres of water are poured into an aquarium of dimensions 50cm length, 30cm breadth, and 40cm height. How high (in cm) will the water rise?
(1 litre = 1000cm3)
?) 6
?) 10
?) 8
?) 20
?) 40
Вопрос id:1931438
In the above correctly worked addition sum, A,B,C and D represent different digits, and all the digits in the sum are different. What is the sum of A,B,C and D?
?) 16
?) 23
?) 18
?) 14
?) 22
Вопрос id:1931439
For how many integer values of n will the value of the expression 4n + 7 be an integer greater than 1 and less than 200?
?) 48
?) 49
?) 51
?) 52
?) 50
Вопрос id:1931440
If f(x) = x² - 3, where x is an integer, which of the following could be a value of f(x)?
I 6
II 0
III -6
?) I, II and III
?) II and III only
?) I only
?) I and II only
?) I and III only
Вопрос id:1931441
-20 , -16 , -12 , -8 ....
In the sequence above, each term after the first is 4 greater than the preceding term. Which of the following could not be a term in the sequence?
?) 200
?) 0
?) 668
?) 440
?) 762
Вопрос id:1931442

?) 1/5
?) 64
?) 64 / 5
?) 6³
?) 6/5
Вопрос id:1931443
If pqr = 1 , rst = 0 , and spr = 0, which of the following must be zero?
?) Q
?) S
?) R
?) T
?) P
Вопрос id:1931444
√5 percent of 5√5 =
?) 0.25
?) 0.5
?) 25
?) 2.5
?) 0.05
Вопрос id:1931445
The distance from town A to town B is five miles. C is six miles from B. Which of the following could be the distance from A to C?
I 11
II 1
III 7
?) I, II, or III
?) II only
?) II and III only
?) I only
?) I and II only
Вопрос id:1931446
  If the radius of the circle with centre O is 7 and the measure of angle AOB is 100, what is the best approximation to the length of arc AB ?
 
?) 10
?) 13
?) 9
?) 12
?) 11
Вопрос id:1931447
  All the dots in the array are 2 units apart vertically and horizontally. What is the length of the longest line segment that can be drawn joining any two points in the array without passing through any other point ?
?) √20
?) √10
?) 3
?) 2√2
?) 2
Вопрос id:1931448
A dress on sale in a shop is marked at $D. During the discount sale its price is reduced by 15%. Staff are allowed a further 10% reduction on the discounted price. If a staff member buys the dress what will she have to pay in terms of D ?
?) 0.75D
?) 0.775D
?) 0.765D
?) 0.805D
?) 0.76D
Вопрос id:1931449
n is an integer chosen at random from the set
{5, 7, 9, 11 }

p is chosen at random from the set
{2, 6, 10, 14, 18}

What is the probability that n + p = 23 ?
?) 0.1
?) 0.3
?) 0.25
?) 0.4
?) 0.2
Вопрос id:1931450
What is the length of the line segment in the x-y plane with end points at (-2,-2) and (2,3)?
?) 3
?) √41
?) 9
?) √31
?) 7
Вопрос id:1931451
A perfect cube is an integer whose cube root is an integer. For example, 27, 64 and 125 are perfect cubes. If p and q are perfect cubes, which of the following will not necessarily be a perfect cube?
?) pq + 27
?) 8p
?) -p
?) pq
?) (p - q)6
Вопрос id:1931452
A certain animal in the zoo has consumed 39 pounds of food in six days. If it continues to eat at the same rate, in how many more days will its total consumption be 91 pounds?
?) 12
?) 11
?) 8
?) 10
?) 9
Вопрос id:1931453
One side of a triangle has length 8 and a second side has length 5. Which of the following could be the area of the triangle?
I 24
II 20
III 5
?) II and III only
?) I, II and III
?) I only
?) II only
?) III only
Вопрос id:1931454
If n is even, which of the following cannot be odd?
I n + 3
II 3n
III n² - 1

?) I only
?) III only
?) I, II and III
?) II only
?) I and II only
Вопрос id:1931455
If a² = 12, then a4 =
?) 24
?) 72
?) 16
?) 36
?) 144
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