If You weren't able to finish high school for any reason,

solutions - S A T

1) What is the unit digit of the following products? 

  a.  6 ²⁺ⁿ  (n is +ive)

  b.  11³⁵ x 456 

  c.  4²⁰⁵

  d.  4²¹²

  e.  7² x 5⁹⁴

      a. 6      b. 6      c. 4      d. 6      e. 5

2) In a barber shop the number of customers come at least 10 more than 0.25 of this fraction come in video shop. Determine an inequality supposing b customers for barber and v for video shop.

                                                 v/4 + 10  < b

3) If 0 < a ,  b < 0, then:

   a) a + b = 0             c) a + b < 0                

   b) a / b < 0               d) a + b > 0

   e) ab > 0

                                    b) is true

4) If x is less than zero and y is less than zero, then: (correct answer is underlined)

  a.  x(y) = 0  False/True        c. y _ x > 0 False/True

  b. x + y < 0 False/True        d. y + x > 0 False/True

        xy

5) If f(x) = x/2 _ 5, c = ?                     f(x)         x  

   (see the chart)                                0         10

   Second column is the value        9            d

   Of x & first column is the              d            c

   Solution of equation.

            d= 28,             c=66

6) If (x) = 1 + 2x, find variables:

f(x)         x

3            1

a           0.5

13          b

1            c

                         a = 2,        b = 13,         c = 0

7) Radius and height of a circular cylinder are decreased by 20% and 50% respectively. What percent the volume be decreased?

                                                              big      small

V of big cylinder = 1,000,000 p        cyl        cyl

V of small cylin.  =   320,000 p      r=100     r=80

   Net decrease   =   680,000           h=100    h=50

   % decrease            68%

8) Side of a square is increased by 30%. What percent its area be increased?         

                                                            Small      Big

V of big square= 16900                   Sqr.        Sqr.

V of small sq.  =  10000                100           130

Net increase = 6900

Percent increase = 69%

9) Two points M and N have the following coordinates: M(b, -b),  N(5a, 5a), find the distance from A to B.  Note: consider * as the sign of sq root

AB = * (X₂ _ X₁) + (Y₂ _ Y₁) ²     

AB =  * 2(25a² + b²)

10) A(1, 0), B(8, 0) and C(1, -4) are three vertices of a Rt triangle. Determine the hypotenuse.

            BC since it is the biggest side = 8.1

11) AB is a diameter of a circle where A(d, 0) and B(d, 4c). Area of the circle would be:

a) 0.5 pc²       b) pc²        c) 2 pc²          d) 4 pc²

radius is 2c and area d) 4 pc²

12) Radius of a wheel is 2.5 ft. The wheel rolls along with ground at a rate of 352 revolutions per min. Find the wheel speed miles per hour.

Circumference of wheel: 5 x 3.14

Distance covered in 1 min = 352 x 5 x 3.14 = 1760 x 3.14 ft

   “          “    in 1 hr = 20 x 3.14 or 62.8 miles

13) Circumference of each wheel of an electric lorry is 12 ft. It rolls 0.25 revolution per sec along with smooth ground. What is the speed of lorry in miles per hr.

Speed per sec = 0.25 x 12 = 3 ft

           Per hr = 3 x 3600 = 10800 ft/hr

           10800 divided 5280 = 39 miles / hr

14) 5^{11 - a}  = 625, find a

                                                a = 7

15) What is the rule of sequence?

            1, 3, 7, 15, ___

  A)2^n-1            B)3^n-1              C)4^n-1              D)2^n-1

16) What is the rule of sequence?

            12, 24, 72, 264, ___

  A)12n            B)n¹²               C)12ⁿ              D)4ⁿ⁺⁸

17) What is the rule of sequence?

            3, 5, 7, 9, ___

    A)2ⁿ            B)2n+1           C)2n         D)n² + 1

18) Find the 10^th term of the above sequence

            2(10) + 1 = 21

19) Find 31^st term: 3, 7, 11, 15, ____

            123

20) What is the median of the ten following numbers which are in ascending order:

x,  y,  z,  24,  36,  42,  60,  72,  x+72

median = 36 + 42 = 78 /2 = 39

21) The average (mean) of three even integers a, b, c is 8. What is the median of a, b, c, 20?

b = a+2, c = a+4

1/3(a+a+2+a+4) = 8, then a = 6

Median of 6, 8, 10, 20 is 9

22) Find the mean of the following three terms:

15x² + 9,  3x _ 5,  1 _ 3x

A) 5x² + 1.7          B) 15x² + 5        C) 5 + 3x

23) Average score of my sister after 5^th examination is 58. How many minimum marks must she obtain in her last 6^th exam to reach the average 70?

                                                70 marks

24) A number is divisible by 6 and 15. It could also be divisible by:

a) 45               b) 30               c) 20               d) 12

25) If x + y < 10, and x - y > 12, which of the following pairs could be the values of x and y?

a.(-9, 9)           b.(10, -2)          c.(9, -1)

26) A special lottery is to be held to select the student. There are 100 seniors, 150 juniors, and 200 sophomores who applied. Each senior's name is placed in the lottery 3 times; each junior's name 2 times; and each sophomore's name 1 time. What is the probability that a senior's name will be chosen?

                                                3/8

27) 4^-(x+2)  = 4^-3       find x

                                                            X = 1

28) b and r are positive integers and b² = r + 12, Is r supposed to be equal to 2, 3 4, 5 or 6?

The only possible value for r is “4” while both variables are +ive.

29) a³ = b² _ 2, find the value of a and b   if a = b < 0

 A) 1                B) -1                C) 2                 E)-2

30) If x = -ive and y = +ive, then:

A) x + y > 0

B) x² + y² < 0

C) xy > 0

D) x divided y < 0

E) x _ y > 0

Suppose any –tive value for x and +ive for y, we get correct answer D)

31) A rectangular solid has a length = 8, width = 8, height = 12. It is divided into 12 cubes. What is the edge of each cube?

Volume of rectangular solid = 8 x 8 x 12 = 768

Volume of each cube = 768 divided 12 = 64

Side of each cube = (64) ^1/3 = 4

   [Formula V of cube = s³ ]

32) Each side of a cube is 2.5 units, Its volume?

            V = 15.6 sq unit

33) What is the perimeter of a square ABCD having diagonal 6?

Let the center of the square O, then AOB is a Rt triangle. AB = *3² + *3² = 3*2 (each side)

Perimeter = 12*2  (consider the sign * as sq. root)

34) According to an entry-record total 300 people came in an amusement park. One person could choose his/her one favorite ride. Entry of 10 persons was not made (undecided). What would be the most possible entry of Ride F while x and y both are not equal to zero?

                        RIDE           NUMBER OF PEOPLE

                        Ride A            90

                        Ride B            71

                        Ride C            19

                        Ride D            45

                        Ride E            x

                        Ride F             y

Total entries = 290

Entries left = 290 - (90+71+19+45) = 65

We are bound to give at least 1 entry to Ride E because x is not zero.

Maximum possible entries for Ride F = 65 _1 = 64

35) XY is the diameter of a circle; X(d, 0),  Y(d, 4c); Area of the circle would be:

  A) 0.5 x 3.14 c²                   B) 3.14 x c²

  C) 2 x 3.14 c²                     D) 4 x 3.14 c²           E) 16 x 314c²

AB = *(d-d) ² + (4c-0) ² = 4c (which is diameter)  Area = 3.14 (2c)² = 4 x 3.14c²

36) Three vertices of a triangle are M(0,5), P(2,-7) and R(-3,8); which side is the biggest?

A) RM                         B) RP                         C) PM

37) When 80 divided by 9, remainder is r

      When r divided by 3, remainder is n;  find r x n

    8                                 2  

 9)80                           3)8

    72                               6

      8 = r                         2 = n         r x n = 16

Questions 38 thru 41; determine the rule of sequence:-

38) 12, 24, 72, 264, ___

A) 12n             B) n¹²              C) 12ⁿ            

D) 4ⁿ⁺¹            E) 4ⁿ + 8

39) 1, 3, 7, 15,  ___

A) 2^n-1             B) 3 ^n-1            C) 4 ^n-1 

D) 2 ^n-1            E) n ²⁺¹

40) 2, 5, 7, 9, ___

A) 2 ⁿ              B) 2n+1          C) 2n 

D) n ² + 1        E) n ² + 1

41) Find the 11^th term of the above sequence

            21

42) The average (mean) of three even integers a, b, c is 8. What is the median of a, b, c, 20?

1/3(a+a+2+a+4) = 8;  a=6

Median of 6, 8, 10, 20 is 9

43) Average of four odd numbers is 16, find them.

 0.25 (a+a+2+a=4+a=6) = 16

Numbers are 13, 15, 17, 19

44) What is the average (arithmetic mean) of all the multiples of ten from 10 to 190 inclusive?

                                100

45) A cubical block of metal weighs 5 pounds. How much will another cube of the same metal weigh if its sides are twice as long?

Suppose the side was a, then its volume was a³

Now its side is twice i.e. 2a, its volume would be 8a³ i.e. 8 times of previous volume. Similarly its weight would be 8 times i.e. 5 x 8 = 40

46) Solve: (Ö5 -  Ö6) ² 

                                            1 - 2Ö30

47) Simplify: 2¹⁰ + 2¹⁰ + 2¹⁰ + 2¹⁰

A) 2⁴⁰              B) 8¹⁰             C) 2¹²

48) Helpers are needed in a bakery for a special order of 24 large cakes and 420 small cakes. One helper can prepare 2 large cakes and 35 small cakes in an hour. How many helpers are needed if kitchen is available for only 3 hours?

Large cake denoted L and small cake S,

In 3 hrs each helper can make       6L + 105 S

In 3 hrs 4 helpers can make           24L + 420S

49) Ratio between the ages Ali and Jeo is 2:3 and between Jeo and Sam is 6:1. What is the ration between the ages of Ali and Sam?

                                                                 4:1

50) A rectangle measuring 3 x 4 inches is inscribed in a circle. Area of the circle=?

                                                19.6 sq in

51) 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?

a+a+1+a+2+a+3 = 4a + 6 (sum of smaller integers)

a+3+a+4+a+5+a+6 = 4a + a8 (sum of bigger integers, a+3 is common)

difference = 12

52) 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?

                                8 inches

53) n and m are positive. 2n is the square of a number and 9nm is the cube of a number. The smallest value for n + m is:

A) 13         B) 11         C) 8          E) 7

                                    (n is 2 and m is 6)

54) a = x + y and b = x, then a ratio b is:

                 y

x + y / xy

55) You have a hundred dollars in dollar bills. You are going to divide it up (unequally) among four people. You  want everyone to get a whole number of dollars and you don’t want any money left over. To fulfill

these conditions, you can divide the money according to which of the following ratios?

I. 4 : 3 : 2 : 1

II. 10 : 5 : 2 : 1

III. 9 : 7 : 3 : 1

(A) I, only

(B) II, only

(C) I and II, only

(D) I and III, only

(E) II and III, only