MU-NLPC/Calc-aqua_rat huggingface dataset:
For any integer n greater than 1, #n denotes the product of all the integers from 1 to n, inclusive. How many prime numbers are there between #6 +2 and #6 +6 , inclusive? Choose the correct choice from the following answers:
A) None B) One C) Two D) Three E) Four

Solution: Given that n* denotes the product of all the integers from 1 to n, inclusive so, 6*+2=6!+2 and 6*+6=6!+6.   Now, notice that we can factor out 2 our of 6!+2 so it cannot be a prime number, we can factor out 3 our of 6!+3 so it cannot be a prime number, we can factor out 4 our of 6!+4 so it cannot be a prime number, ... The same way for all numbers between 6*+2=6!+2 and 6*+6=6!+6, inclusive. Which means that there are no primes in this range.   Nonenswer: None.
Answer: A
A circular rim 35 inches in diameter rotates the same number of inches per second as a circular rim 42 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim makes in terms of x ?
Choose the correct choice from the following
A) 48pi/x B) 50x C) 48x D) 24x E) x/75

Solution: C = (pi)d   C(small): (pi)*35   C(large): (pi)*42   Lets say the time horizon is 60 seconds, so during that time the smaller rim covers a distance of (pi)*35*60 = (pi)*(2100) inches   (pi)*(2100) = (pi)*(42)(x)   pi*(50) = pi*(x)   50=x   Answer: 50x.
Answer: B
If the integer p is rounded to the nearest hundred, the result represents a 66 2/3 % increase over the value obtained when p is rounded to the nearest ten. which of the following is a possible value of p?	Choose the correct option: A) 64 B) 67 C) 99 D) 133 E) 147

Solution: We have to check options 1 by 1.   64 rounded to nearest hundred = 100   64 rounded to nearest ten = 60   now difference = 40   the result represents a 66 2/3 % increase over the value obtained when x is rounded to the nearest ten.   therefore 40/60)*100 = 66 2/3 ==>this is the answer.   99 rounded to nearest ten = 100   133 rounded to nearest ten = 130   133 rounded to nearest hundred p= 100=64
Answer: A
A parking garage rents parking spaces for $10 per week or $25 per month. How much does a person save in a year by renting by the month rather than by the week?  Choose one
A) $120	B) $160	C) $220	D) $240	E) $260

Solution: 10$ per week!   An year has 52 weeks.   Annual charges per year = 52* 10= 
52* 10 = 520
520$   30$ per month!   An year has 12 months.   $120nnual charges per year= 12 * 25= 
12 * 25 = 300
300$   520 - 300= 120   $120ns $120
Answer: A
A two years older than B who is twice as old as C. if the total of the ages of A , B and C be 27, the how old B ?	Choose the correct choice:
A) 7 B) 8 C) 9 D) 10 E) 12

Solution: C's age be X years. the B's age = 2X years, A's age= (2X+2)years   therefore (2X+2)+2X+X=27   5X=25   X=5   B's age 2X=10 years. correct answer (10)
Answer: D
The symphony sells two kinds of tickets: orchestra, for $30, and upper tiers, for $12. On a certain night, the symphony sells 90 tickets and gets $1836 in revenue from the sales. How many orchestra tickets did they sell?  Select
A) 38	B) 42	C) 46	D) 50	E) 54

Solution: Let x be the number of orchestra tickets.   Then 90-x is the number of upper tier tickets.   30x + 12(90-x) = 1836   18x = 1836-1080   x = 42   The answer is 42.
Answer: B
Pipe A can fill a tank in 8 hours, pipe B in 16 hours and pipe C in 16 hours. If all the pipes are open, in how many hours will the tank be filled? Choose the correct choice from the following answers:
A) 2
B) 3
C) 4
D) 5
E) 6

Solution: Part filled by A + B + C in 1 hour = 1/8 + 1/16+ 1/16= 1/4   All the three pipes together will fill the tank in 4 hours.   Answer: 4
Answer: C
Express 25 mps in kmph? Choose the correct option: A) 299 B) 29 C) 90 D) 77 E) 11

Solution: 25 * 18/5= 
25 * 18/5 = 90
90 kmph Answer:90
Answer: C
X, Y, and Z are different prime numbers. The product X^3*Y^2*Z^2 is divisible by how many different positive numbers? Choose the most appropriate option.
A) 24	B) 36	C) 48	D) 60	E) 72

Solution: The exponents of X^3*Y^2*Z^2 are 3, 2, and 2.   The number of factors is (3+1)(2+1)(2+1) = 36   The answer is 36.
Answer: B
If x is an integer, then x(x - 1)(x - b) must be evenly divisible by three when b is any of the following values EXCEPT  Select the correct option:
A) -4
B) -2
C) -1
D) 2
E) 5

Solution: here's another approach   x(x - 1)(x - b)   all three are consecutive, so the product MUST be a multiple of 3   we don't know the value of b just yet ... so let's extend the series ... the extension itself reveals the answers   ..(x-5)..(x-2)(x-1)x(x+1)..(x+4)..   we can see the possible values of b too from the series   b = 2 OR 2+3n [25]   b = -1 OR -1+3n [-1-4]   B i.e. -2 does not fit in any value of b   so -2 it is
Answer: B
What is the speed of the train in km/hr whose length is 360 metres which passes a pole in 18 seconds? Choose the correct choice from the following answers: A) 59/9 km/hr B) 50/9 km/hr C) 25/6 km/hr D) 55/18 km/hr E) 60/18 km/hr

Solution: Speed=(18x5/18)=5 m/sec.   Length of the train= 360 metre   Time=18s   Speed=length / time   Speed=(360/8)=20 m/sec = 20*5/18 km/hr = 50/9 km/hr   Answer: 50/9 km/hr
Answer: B
A man is walking at the rate of 8 km/hr crosses a bridge in 15 minutes. The length of the bridge is  Choose one.
A) 1000 meters  B) 1050 meters  C) 1200 meters  D) 2000 meters  E) None of these

Solution: Explanation:   We need to get the answer in meters. So we will first of change distance from km/hour to meter/sec by multiplying it with 5/18 and also change 15 minutes to seconds by multiplying it with 60.   Speed=8âˆ—5/18=20/9m/sec   Time=15âˆ—60seconds=900seconds   2000 metersistance=Timeâˆ—Speed/2000 metersistance=20/9âˆ—900=2000meter   Option 2000 meters
Answer: D
Rahul's mother is the only daughter of Monika's father. How is Monika's husband related to Rahul ?
Choose the correct answer:
A) Uncle
B) Father
C) Grandfather
D) Brother
E) SISTER

Solution: Explanation:   Clearly, the only daughter or Monika's father is Monika herself   So, Rahul's mother is Monika   Thus, Monika's husband is the father of Rahul.   Answer: Father) Father
Answer: B
Three partners shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 8 months and 7 months respectively. What was the ratio of their investments?  Pick:
A) 5 : 7 : 8 B) 20 : 49 : 64 C) 38 : 28 : 21 D) None of these E) Cannot be determined

Solution: Solution: Let their investments be Rs. x for 14 months, Rs. y for 8 months and Rs. z for 7 months respectively.   Then, 14x : 8y : 7z = 5 : 7 : 8.   Now, 14x/8y = 5/7 => 98x = 40y   => y = 49/20 x   And, 14x/7z = 5/8   => 112x = 35z   => z = 112/35 x = 16/5 .x.   So x : y : z = x : 49/20 x : 16/5 x = 20 : 49 : 64.   Answer: Option 20 : 49 : 64
Answer: B
In 1982 and 1983, Company B’s operating expenses were $12.0 million and $14.0 million, respectively, and its revenues were $15.6 million and $18.8 million, respectively. What was the percent increase in Company B’s profit (revenues minus operating expenses) from 1982 to 1983 ?	Select
A) 3%	B) 16 2/3%	C) 25%	D) 33 1/3%	E) 60%

Solution: Profit in 1982=15.6-12.0= 
15.6-12.0 = 3.6
3.6   profit in 1983=18.8-14.0= 
18.8-14.0 = 4.8
4.8   increase in profit=4.8-3.6= 
4.8-3.6 = 1.2
1.2   percentage increase   12*100/36=33.33 ; ANSWER:33 1/3%
Answer: D
Two trains of equal lengths are running at speeds of 30 kmph and 60 kmph. The two trains crossed each other in 30 seconds when travelling in opposite direction. In what time will they cross each other when travelling in the same direction? Select
A) 90 sec
B) 18 sec
C) 19 sec
D) 15 sec
E) 11 sec

Solution: Let the length of each train be x m.   (x + x) / (60 + 30)5/18 = (750 * 18) / (30 * 5)= 
(750 * 18) / (30 * 5) = 90
90 sec.   90 secnswer:90 sec
Answer: A
An accurate clock shows 8 o’clock in the morning. Through how many degrees will the hour hand rotate when the clock shows 2 o’clock in the afternoon?	Choose the correct choice from the following.
A) 144° B) 150° C) 168° D) 180° E) None of these

Solution: Angle traced by the hour hand in 6 hours   = (360⁄12 × 6)° = 180°   Answer 150°
Answer: B
(786×74) ÷ ? = 3635.25 Choose one.
A) A)4.8  B) B)48  C) C)16  D) D)68  E) E)48

Solution: Explanation:   58164/x = 3635.25 => x = 58164/3635.25= 
58164/3635.25 = 16
16   Answer: Option 16
Answer: C
Sides of a rectangular park are in the ratio 3: 2 and its area is 3750 sq m, the cost of fencing it at 50 ps per meter is? Options:
A) Rs.150 B) Rs.100 C) Rs.125 D) Rs.175 E) Rs.275

Solution: 3x * 2x = 3750 => x = 25   2(75 + 50) = 250 m   250 * 1/2 = Rs.125   ANSWER:Rs.125
Answer: C
There are two cars. One is 300 miles north of the other. Simultaneously, the car to the north is driven westward at 20 miles per hour and the other car is driven eastward at 60 miles per hour. How many miles apart are the cars after 5 hours?	Select the correct option.
A) 300
B) 360
C) 400
D) 450
E) 500

Solution: Here, drawing a quick sketch of the 'actions' described will end in a diagonal line that you canbuilda right triangle around:   The right triangle will have a base of 400 and a height of 300. The hidden pattern here is a 3/4/5 right triangle (the 300 lines up with the '3' and the 400 lines up with the '4'). In this way, you can deduce that each side is '100 times' bigger than it's corresponding side:   3/4/5 becomes   300/400/500   Thus the distance between the two cars is the length of the hypotenuse of this larger right triangle...   Final Answer:500
Answer: E
The average salary of all the workers in a workshop is Rs.8000. The average salary of 7 technicians is Rs.10000 and the average salary of the rest is Rs.6000. The total number of workers in the workshop is
Choose the correct choice:	A) 20	B) 21	C) 22	D) 23	E) 14

Solution: Solution   Let the toatl number of workers be x.   Then 8000x=(10000 x 7) + 6000 (x -7)   x= 14.   Answer 14
Answer: E
A and B go around a circular track of length 600 m on a cycle at speeds of 36 kmph and 60 kmph. After how much time will they meet for the first time at the starting point? Choose the correct choice from the following answers:
A) 120 sec B) 176 sec C) 178 sec D) 187 sec E) 180 sec

Solution: Time taken to meet for the first time at the starting point   = LCM { length of the track / speed of A , length of the track / speed of B}   = LCM { 600/ (36 * 5/18) , 600/ (60 * 5 /18) }   = 180 sec.   Answer: 180 sec
Answer: E
A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long?
Choices:
A) 80 sec  B) 89 sec  C) 99 sec  D) 86 sec  E) 85 sec

Solution: Explanation:   Speed = (240/24) m/sec = 10 m/sec.   Required time =[ (240 + 650)/10) ] sec = 89 sec.   Answer:89 sec
Answer: B
There are k members in a certain department, including Michael. Two representatives are to be selected to attend a company conference. If there are 55 possible combinations in which Michael is not selected, what is the value of k?	Choose the correct choice from the following choices
A) 11
B) 12
C) 15
D) 18
E) 22

Solution: Combinations of two persons, in which Michael was not selected = 55   number of ways two persons can be selected from m people = m*(m-1)/2   Let m be the number of people excluding Michael, then m*(m-1) = 110 => m=11   Thus, k = m + 1(Michael) = 12   option 12
Answer: B
A circular rim 20 inches in diameter rotates the same number of inches per second as a circular rim 30 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim makes in terms of x ? Choose the correct choice from the following options.
A) 40x
B) 75x
C) 48x
D) 24x
E) x/75

Solution: Revolutions - circumference of the rim.   => 20pi*X*60 = 30pi*Revolutions   => 2/3 *X *60 = Revolutions => 40X - Option 40x
Answer: A
If a coin has an equal probability of landing heads up or tails up each time it is flipped , what is the probability that the coin will land Tails up exactly once in 3 consecutive flips ?  Choose the correct answer
A) 0.125 B) 0.375 C) 0.325 D) 0.5 E) 0.666

Solution: Total number of ways in which H or T can appear in 3 tosses of coin is   = 2 * 2 * 2= 
2 * 2 * 2 = 8
8 ways   For 2 T and 1 TH   Thus probability is= P(HTT) + P(TTH) + P(THT)   = 1/8 + 1/8 + 1/8   = 3/8= 
3/8 = 3/8 = around 0.375
.375   Answer :0.375
Answer: B
Which is smallest prime number? Choose the correct answer:
A) 37
B) 47
C) 24
D) 67
E) 107

Solution: 37nswer:37
Answer: A
A man sitting in a bullet train which is travelling at 50 kmph observes that a goods bullet train , travelling in opposite direction, takes 9 seconds to pass him. If the goods bullet train is 280 m long, find its speed.?
Choose the correct choice from the following.
A) 44 kmph.  B) 52 kmph.  C) 75 kmph.  D) 83 kmph.  E) 62 kmph.

Solution: E   62 kmph.   Relative speed = 280/9 m / sec = ((280/9)*(18/5))= 
((280/9)*(18/5)) = 112
112 kmph.   Speed of goods train= (112 - 50)= 
(112 - 50) = 62
62 kmph.
Answer: E
Two integers are in the ratio of 1 to 4. If 12 is added to the smaller number, the ratio becomes 1 to 2. Find the larger integer.  Select the correct option: A) 8 B) 16 C) 32 D) 48 E) 54

Solution: One option is to set up the equations and solve:   If the ratio of two integers x and y is 1 to 4, then 4x=y, where x is the smaller integer.   If adding 12 to the smaller integer makes the ratio 1 to 2, then 2(x+12)=y.   Substituting y=4x into the second equation yields 2x+24=4x.   So, x=12 (smaller integer) and, y=4x=48 (larger integer) so D is the correct answer.   Another option is to TEST the answer choices.   A) the larger number is 8   Given: the two integers are in the ratio of 1 to 4   So, the smaller number must be 2   If 12 is added to the smaller number, the ratio becomes 1 to 2   If we add 12 to the smaller number (2), we get 14.   So, the new ratio is 14 to 8 which is the same as 7 to 4.   No good. We want a resulting ratio of 1 to 2   ELIMINATE A   B) the larger number is 16   Given: the two integers are in the ratio of 1 to 4   So, the smaller number must be 4   If 12 is added to the smaller number, the ratio becomes 1 to 2   If we add 12 to the smaller number (4), we get 16   So, the new ratio is 16 to 16 which is 1 to 1.   No good. We want a resulting ratio of 1 to 2   ELIMINATE B   C) the larger number is 32   Given: the two integers are in the ratio of 1 to 4   So, the smaller number must be 8   If 12 is added to the smaller number, the ratio becomes 1 to 2   If we add 12 to the smaller number (8), we get 20   So, the new ratio is 20 to 32 which is 5 to 8.   No good. We want a resulting ratio of 1 to 2   ELIMINATE C   D) the larger number is 48   Given: the two integers are in the ratio of 1 to 4   So, the smaller number must be 12   If 12 is added to the smaller number, the ratio becomes 1 to 2   If we add 12 to the smaller number (12), we get 24   So, the new ratio is 24 to 48. This is the same as the ratio of 1 to 2   Therefore (D) is correct   E) the larger number is 54   Given: the two integers are in the ratio of 1 to 4   So, the smaller number must be 13.5 (which is not an integer)   Since both numbers are integers, the larger number cannot be 54.   ELIMINATE E   Therefore 48 is the only correct choice.
Answer: D
On a sum of money, the simple interest for 2 years is Rs. 324, while the compound interest is Rs. 340, the rate of interest being the same in both the cases. The rate of interest is
Choose the correct option
A) 15%  B) 14.25%  C) 9.87%  D) 10.5%  E) 11.5%

Solution: The difference between compound interest and simple interest on Rs. P for 2 years at R% per annum   = (R Ã— SI)/(2 Ã— 100)   Difference between the compound interest and simple interest = 340 - 324= 
340 - 324 = 16
16   (R Ã— SI)/(2 Ã— 100)= 16   (R Ã— 324)/(2 Ã— 100) = 16   R = 9.87%   Answer: Option 9.87%
Answer: C
A two-digit number is such as the product of the digits plus the sum of the digits
is equal to the number. What is the number?	Choose the correct choice from the following options.
A) num 1  B) num 3  C) num 5  D) num 7  E) num 9

Solution: Assume the 2 digit number is of the form xy, with x 6= 0. The statement indicates   that these two digits satisfy the equation xy + x + y = 10x + y. A quick simplification gives y = 9.   correct answer num 9
Answer: E
The reflex angle between the hands of a clock at 10.25 is:
Choose the correct choice from the following answers:	A) 180º	B) 192	1/2 º	C) 195º	D) 197	1/2 º	E) 197 º

Solution: Angle traced by hour hand in 125/12 hrs ={(360/12)x(125/2)}º	= 312 1/2 º	. Angle traced by minute hand in 25 min =(360/60)x 25	º= 150º. Reflex angle = 360º -(312	1/2- 150º	)= 360º - 162 1/2º= 197 1/2º	.Answer: 197	1/2 º
Answer: D
The two trains of lengths 400 m, 600 m respectively, running at same directions. The faster train can cross the slower train in 180 sec, the speed of the slower train is 48 km. then find the speed of the faster train?	Choose the correct choice.
A) 60 B) 68 C) 67 D) 69 E) 70

Solution: Length of the two trains = 600m + 400m   Speed of the first train = X   Speed of the second train= 48 Kmph   1000/X - 48 = 180   1000/x - 48 * 5/18 = 180   50 = 9X - 120   X = 68 Kmph   Answer: Option 68
Answer: B
Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1120?	Choose the correct choice:
A) 1000
B) 2217
C) 2889
D) 2777
E) 2991

Solution: 1120 = P [1 + (5*12/5)/100]   P= 1000   1000nswer: 1000
Answer: A
Today my car meter reads as 72927 kms. I notes that this is a palindrome. How many minimum kms i need to travel so my car meter find another palindrom.  Choose the correct option: A) 100 kms B) 115 kms C) 110 kms D) 210 kms E) 120 kms

Solution: 110 kms   110 kms    72927+110= 
 72927+110 = 73_037
73037 , a palindrome
Answer: C
The difference between the place value and the face value of 9 in the numeral 856973 is Choose one
A) 973 B) 891 C) 5994 D) 6084 E) None of these

Solution: (Place value of 9) - (Face value of 9) = (900 - 9)= 
(900 - 9) = 891
891   Answer: Option 891
Answer: B
The number of people who purchased book A is twice the number of people who purchased book B. The number of people who purchased both books A and B is 500, which is twice the number of people who purchased only book B. What is the number of people X who purchased only book A?  Choose the correct choice from the following options:
A) 250
B) 500
C) 750
D) 1000
E) 1500

Solution: This is best solved using overlapping sets or a Venn Diagram. We know that A = 2B, and that 500 people purchased both A and B. Further, those purchasing both was double those purchasing B only. This gives us 250 people purchasing B only. With the 500 that pruchased both, we have a total of 750 that purchased B and this is 1/2 of those that purchased A. So, 1500 purchased A. Less the 500 that purchased both, X=1000 purchased A only. (This is much simpler to solve using the Venn diagram).   Correct answer is D. 1000
Answer: D
Look at this series: __, VIII, XI, XIV, XVII, XX, ... What number should fill the blank? Choose the correct choice from the following options:	A) IX	B) XXIII	C) XV	D) V	E) None

Solution: Explanation: This is a simple addition series; each number is 3 more than the previous number.   Answer: V
Answer: D
The variable x is inversely proportional to the square of the variable y. If y is divided by 7a, then x is multiplied by which of the following?
Choose one.
A) 1/49a B) 1/49a^2 C) 1/7a D) 49a E) 49a^2

Solution: initially - did x= 1/y^2   But this yielded the wrong answer,   I then re examined the question and tried y^2/x =1   Which I then got y = SQR(X)   subbing into y/7a I got answer 49a^2)
Answer: E
A certain sum of money at simple interest amounted Rs.1200 in 12 years at 6% per annum, find the sum?  Options
A) 337
B) 268
C) 198
D) 697
E) 168

Solution: 1200 = P [1 + (12*6)/100]   P = 697'   Answer:697
Answer: D
The regular price per can of a certain brand of soda is $0.60. If the regular price per can is discounted 20 percent when the soda is purchased in 24-can cases, what is the price of 72 cans of this brand of soda purchased in 24-can cases? Select the correct option: A) $16.32 B) $18.00 C) $21.60 D) $34.56 E) $28.80

Solution: The discounted price of one can of soda is (0.8)($0.60), or $0.48   Therefore, the price of 72 cans of soda at the discounted price would be (72)($0.48) = 34.56   Answer: $34.56.
Answer: D
Look at this series: 2, 3, 4, 9, 8,... What number should come next?	Choose the correct choice from the following options.
A) 128 B) 64 C) 16 D) 32 E) 27

Solution: Explanation: The given series is obtained by increasing powers of 2 and 3.   2*1= 
2*1 = 2
2   3*1= 
3*1 = 3
3   2*2= 
2*2 = 4
4   3*3= 
3*3 = 9
9   2*2*2= 
2*2*2 = 8
8   3*3*3= 
3*3*3 = 27
27 and so on.   Answer: Option 27
Answer: E
Positive integer y is 50 percent of 50 percent of positive integer x, and y percent of x equals 36. What is the value of x?	Choose the correct choice from the following answers:
A) 80	B) 96	C) 100	D) 108	E) 120

Solution: y = 0.5*0.5*x = x/4   y%*x = 36   (y/100)*x = 36   (x/400)*x = 36   x^2 = 36*400   x = 120   The answer is 120.
Answer: E
Tough and Tricky questions: Decimals.
The value of x is derived by summing a, b, and c and then rounding the result to the tenths place. The value of y is derived by first rounding a, b, and c to the tenths place and then summing the resulting values. If a = 5.45, b = 2.95, and c = 3.74, what is y – x?
Choose one:
A) -0.1
B) 0
C) 0.05
D) 0.2
E) 0.3

Solution: To find x, we first sum a, b, and c, then round to the tenths place. 5.45 + 2.95 + 3.74 = 12.14, which rounds to 12.2.   To find y, we first round a, b, and c to the tenths place and them sum them. so 5.4 + 2.9 + 3.7 = 12.0.   We are looking for y - x, which gives us  12.2 - 12.0= 
 12.2 - 12.0 = 0.2
0.2, or answer choice 0.2.
Answer: D
A, B and C are partners in a business. Their capitals are respectively, Rs.5000, Rs.6000 and Rs.4000. A gets 30% of the total profit for managing the business. The remaining profit is divided among three in the ratio of their capitals. In the end of the year, the profit of A is Rs.200 more than the sum of the profits of B and C. Find the total profit.  Choose the correct choice from the following:
A) Rs.4500
B) Rs.5200
C) Rs.1800
D) Rs.3000
E) Rs.5000

Solution: A:B:C = 5:6:4   Let the total profit = 100 - 30= 
100 - 30 = 70
70   5/15 * 70= 70/3   A share = 70/3 + 30 = 160/3   B + C share = 100 - 160/3 = 140/3   A-(B+C) = 160/3 - 140/3 = 20/3   20/3 ---- 200   100 ---- ? => 3000   ANSWER:Rs.3000
Answer: D
Two trains 111 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 100 km and the other at the rate of 120 kmph. In what time will they be completely clear of each other from the moment they meet?	Choose the correct choice from the following answers:
A) 4.85	B) 7.85	C) 4.51	D) 5.85	E) 6.15

Solution: T = (111 + 165)/ (100 + 120) * 18/5   T = 4.51   ANSWER:4.51
Answer: C
A can give B 100 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race?
Choose one:
A) 111.12 m	B) 161.12 m	C) 111.82 m	D) 111.19 m	E) 131.12 m

Solution: A runs 1000 m while B runs 900 m and C runs 800 m.   The number of meters that C runs when B runs 1000 m,   = (1000 * 800)/900   = 8000/9   = 888.88 m.   B can give C   = 1000 - 888.88= 
1000 - 888.88 = 111.12
111.12 m.   111.12 mnswer:111.12 m
Answer: A
106 x 106 - 94 x 94 = ? Pick one:
A) 2400 B) 2000 C) 1904 D) 1906 E) None of them

Solution: =(106)^2-(94)^2   =(106+94)(106-94)   =(200 x 12)   =2400   2400nswer is 2400
Answer: A
What is the value of n if the sum of the consecutive odd integers from 1 to n equals 169?	Choose the correct choice.
A) 47  B) 25  C) 37  D) 33  E) 29

Solution: # of terms = (n-1/2)+1 {(last term - first term)/2+1|   Sum = (1+n)/2 * # of terms   = (n+1)^2/4= 169   n+1 = 13*2   n+1 = 26   n=25.   ANSWER:25
Answer: B
Which of the following describes all values of x for which 4-x^2 ≥ 0 ?	Select the correct option
A) x ≥ 1  B) x ≤ -1  C) 0 ≤ x ≤ 1  D) x ≤ -1 or x ≥ 1  E) -2 ≤ x ≤ 2

Solution: 4-x^2 >= 0 ---> x^2-4<=0   --> (x+2)(x-2)<=0   Above equation true for   i) x+2<=0 and x-2>=0 ---> x<= -2 and x>=2 ---> this is not possible ---Strike out this solution   ii) x+2>=0 and x-2<=0 ---> x>=-2 and x<=2 --> -2<=x<=2   Answer -2 ≤ x ≤ 2
Answer: E