MU-NLPC/Calc-aqua_rat huggingface dataset:
Nil and Ethan are brothers. They left their home
at the same time and drove to the same beach.
Nil drove at a speed of 80 miles per hour. Ethan
drove at a speed of 20 miles per hour. Nil
arrived at the beach 0.5 hour earlier than Ethan.
What is the distance between their home and the
beach?  Choose the correct choice from the following answers:
A) 70 miles
B) 80 miles
C) 90 miles
D) 100 miles
E) 110 miles

Solution: Every hour, Nil gets ahead of Ethan  80 - 20= 
 80 - 20 = 60
60 miles. When Nil arrived at the beach, Ethan   is only 20 × 0.5= 10 miles behind. That tells us   they only drove 1 hour when Nil arrived at the   beach.   The distance between their home and the beach   is   Nil’s speed × Nil’s time   = 80 × 1 = 80 miles.   correct answer 80 miles
Answer: B
Solve the equation for x : 6x - 87 + 3x = 4 + 9 - x Pick:  A) 12  B) 5  C) 10  D) 9  E) 3

Solution: 10   10   9 x + x = 13 + 87   10 x = 100 => x = 10
Answer: C
An aeroplane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the same distance in 1 hours, it must travel at a speed of:
Choose the most appropriate option:
A) 300 kmph  B) 360 kmph  C) 600 kmph  D) 720 kmph  E) 750 kmph

Solution: Explanation:   Distance = (240 x 5) = 1200 km.   Speed = Distance/Time   Speed = 1200/(5/3) km/hr.   Required speed =(1200 X 3/5)km/hr	= 720 km/hr.   ANSWER IS 720 kmph
Answer: D
The sum P of the arithmetic sequence a, a+d, a+2d,..., a+(n-1)d is give by Pn = (n/2)*(2a + n-1)d. What is the sum of the integers 1 to 100 inclusive, with the even integers between 25 and 63 omitted. Choose the correct choice from the following answers:
A) 4345
B) 4302
C) 4258
D) 4214
E) 4170

Solution: a method to do it under one minutes is to take advantage of the choices given...   lets work on the last digit as we have different units digit in each choice...   total sum of 1 to 100 inclusive will have 0 as the last digit..   this is so because the resultant will be 10*(sum of all single digits)... and since we are multiplying by 10,units digit will be 0...   now for single digit in sum of even number from 25 to 63..   25 to 65 will have 4 times sum of single digit even int, 4*(2+4+6+8+0)=4*20..   here too the units digit is 0, but 64 has to be excluded from the total..   two ways from here on..   1) we are subtracting 0 from 0   so units digit should be 0, but we have to add 64..   so last/units digit =4..   2)we subtract 64 from sum P of even int..   so units digit=80-4=76..   or units digit =6...   so our answer should have units digit as 10-6=4..   only D has 4 as units digit..   ans 4214
Answer: D
If each year the population of the country grows by 30%, how many years will elapse before the population of the country doubles?  Select:
A) 2
B) 4
C) 5
D) 3
E) 7

Solution: Till Year 2000, population is 100 .   Year 2001: Population becomes 130 ............. 1 Year elapsed   Year 2002: Population becomes 169 ............. 2 Year elapsed   Year 2004: Population > 200 .................. 3 year elapsed   Answer:3
Answer: D
The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.1.50 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost?
Choose the correct option:
A) Rs.1014	B) Rs.1140	C) Rs.999	D) Rs.1085	E) Rs.1020

Solution: a2 = 3136 => a = 56   56 * 4 * 3= 
56 * 4 * 3 = 672
672 – 6= 666 * 1.5= 
666 * 1.5 = 999
999   ANSWER:Rs.999
Answer: C
John read the quarter of the time that Tom read. Tom read only two-fifth of the time that Sasha read. Sasha read twice as long as Mike. If Mike read 5 hours, how long did John read? Choose the correct answer
A) 2 hours	B) 4 hours	C) 1 hours	D) 5 hours	E) 7 hours

Solution: Mike read 5 hours. Sasha read twice as long as Mike. Hence Sasha read:   2 * 5= 
2 * 5 = 10
10 hours   Tom read two-fifths of the time that Sasha read. Hence Tom read:    (2 / 5) * 10= 
 (2 / 5) * 10 = 4
4 hours   John read the quarter of the time that Tom read. Hence John read:     (1 / 4) * 4= 
  (1 / 4) * 4 = 1
1 hour   correct answer 1 hours
Answer: C
The ratio of the number of boys and girls in a college is 7:8. If the percentage increase in the number of boys and girls be 20% and 10% respectively. What will be the new ratio?
Choose the correct choice from the following:
A) 21:29 B) 21:27 C) 21:22 D) 21:23 E) 21:21

Solution: Originally, let the number of boys and girls in the college be 7x and 8x respectively.   Their increased number is (120% of 7x) and (110% of 8x).   i.e., (120/100 * 7x) and (110/100 * 8x)   i.e., 42x/5 and 44x/5   Required ratio = 42x/5 : 44x/5 = 21:22   Answer: 21:22
Answer: C
Given a certain positive integer X, if x is divided by 5 the remainder is 3 and if it is divided by 7 the remainder is 5. What is the remainder when x is divided by 30.  Choose the correct choice from the following choices:
A) 5
B) Between 1 and 4, inclusive
C) Between 5 and 10, inclusive
D) Between 10 and 12, inclusive
E) above 12

Solution: Put in real numbers.   Given number x   5x+3 = 7x+5   Start 5x+3 --> 8, 13, 18, 23, 28, 33,....   Of these only 33 fit the description 7x+5. The remainder when divided by 30 is 3. So answer is B).   If there is a purely algebraic way, please tell.   Answer = Between 1 and 4, inclusive)
Answer: B
If f(x)=2^x and x is a natural number, what CANNOT be the answer to f(x)?
Select the correct option.
A) 2	B) 3	C) 4	D) 8	E) 16

Solution: There is no possible way for a 2 raised to a natural number power to be equal to 3, so the answer is 3.
Answer: B
A certain stationary store arranges notebooks on display such that each of the seven different colors of notebooks white,yellow, orange, green, red, blue, and purple are consecutive in a repeating pattern. If eight consecutively displayed notebooks are purchased, what is the probability that two of the notebooks are purple? Choose the most appropriate option
A) 1/49  B) 1/8  C) 1/7  D) 2/7  E) 1/2

Solution: After white,yellow, orange, green, red, blue, and purple, the next book can be of any given seven colours, therefore we have total seven possibilities, out of which we need purple i.e. 1 therefore prob is 1/7   Answer:1/7
Answer: C
In the xy-coordinate system, if (m, n) and (m + 5, n + k) are two points on the line with the equation x = 2y + 5, then k =  Choose the correct choice from the following answers.
A) 1/2  B) 1  C) 2  D) 5/2  E) 4

Solution: Since (m, n) and (m + 2, n + k) are two points on the line with the equation x = 2y + 5 they should satisfy m=2n +5 and m+5 =2 *(n+k)+5.   By 1st equation we have m-2n=5 and by 2nd equation m-2n = 2k ---> 5=2k --->k=5/2.   The answer is, therefore, (5/2).
Answer: D
A and B together invested Rs. 15,000 in a business. At the end of the year, out of total profit is Rs. 3,000 B's share was Rs. 1000. A's investment was Choose the correct choice from the following answers.
A) s. 4,500	B) s. 8,250	C) s. 9,500	D) s. 10,000	E) s. 12,250

Solution: A+B=15000   total profit=3000   3000-1000= 
3000-1000 = 2_000
2000   2000;1000=2:1   then   2*15000/3= 
  2*15000/3 = 10_000
10000   ANSWER:s. 10,000
Answer: D
A certain company employs 5 senior officers and 4 junior officers. If a committee is to be created, that is made up of 3 senior officers and 1 junior officer, how many different committee are possible?
Choose the correct choice from the following choices.
A) 8  B) 24  C) 58  D) 40  E) 210

Solution: Number of ways to select 3 senior officers from 5 of them = 5C3 = 10 ways   Next we can determine the number of ways to select 1 junior officer.   number of ways to select 1 junior officer from 4 of them = 4C1 = 4 ways   Thus the number of ways to select 3 senior officers and 1 junior officer is 10 x 4 = 40 ways.   Answer: 40
Answer: D
If a positive odd integer N has p positive factors, how many positive factors will 5N have ?
Choose the most appropriate option
A) p  B) 2p  C) P+1  D) 2p+1  E) Cannot be determined

Solution: I have added some extra text to make this question more GMAT-like:   Let's TEST some values of N   Try N = 3   The factors of 3 are {1, 3}. Here, p =2   So, 2N = (2)(3) = 6   The factors of 6 are {1, 2, 3, 6}. So, we have a total of4   Now check the answer choices:   A) p =2No good. We want an output of4. ELIMINATE   B) 2p = (2)(2) = 4. PERFECT! KEEP B   C) P+1 =2+ 1= 
2+ 1 = 3
3 No good. We want an output of4. ELIMINATE   D) 2p+1= (2)(2) + 1 = 5 No good. We want an output of4. ELIMINATE   E) Cannot be determined. POSSIBLE. KEEP E   Let's TEST another value of N   Try N = 7   The factors of 7 are {1, 7}. Here, p =2   So, 2N = (2)(7) = 14   The factors of 14 are {1, 2, 7, 14}. So, we have a total of4   Now check the REMAINING answer choices:   B) 2p = (2)(2) =4. PERFECT! KEEP B   E) Cannot be determined. POSSIBLE. KEEP E   Let's TEST one more (non-prime) value of N   Try N = 9   The factors of 9 are {1, 3, 9}. Here, p =3   So, 2N = (2)(9) = 18   The factors of 18 are {1, 2, 3, 6, 9}. So, we have a total of6   Now check the REMAINING answer choices:   B) 2p = (2)(3) =6. PERFECT! KEEP B   E) Cannot be determined. POSSIBLE. KEEP E   At this point, it SEEMS LIKELY that the correct answer is 2p+1
Answer: D
A certain bus driver is paid a regular rate of $16 per hour for any number of hours that does not exceed 40 hours per week. For any overtime hours worked in excess of 40 hours per week, the bus driver is paid a rate that is 75% higher than his regular rate. If last week the bus driver earned $1032 in total compensation, how many total hours did he work that week?
Choose the correct answer.
A) 36  B) 40  C) 44  D) 48  E) 54

Solution: For 40 hrs = 40*16= 
40*16 = 640
640   54xcess= 1032-640= 
1032-640 = 392
392   For extra hours=.75(16)=12+16= 
12+16 = 28
28   Number of extra hrs=392/28=98/7= 
98/7 = 14
14   Total hrs=40+14= 
40+14 = 54
54   Answer 54 52
Answer: E
In how many seconds will a train 180 meters long pass an oak tree, if the speed of the train is 54 km/hr?	Choose the correct answer:
A) 10
B) 12
C) 14
D) 16
E) 18

Solution: speed = 54 * 5/18= 
54 * 5/18 = 15
15 m/s   time= 180/15= 
180/15 = 12
12 seconds   The answer is 12.
Answer: B
A full stationary oil tank that is a right circular cylinder has a radius of 100 feet and a height of 25 feet. Oil is pumped from the stationary tank to an oil truck that has a tank that is a right circular cylinder until the truck's tank is completely filled. If the truck's tank has a radius of 5 feet and a height of 12 feet, how far (in feet) did the oil level drop in the stationary tank?
Options.
A) 2.5 B) 0.025 C) 0.05 D) 0.03 E) 3

Solution: The volume of oil pumped to the tank = The volume of oil taken away from stationary cylinder.   pi*25*12 = pi*h*100*100 (h is distance that the oil level dropped)   h = 300/10,000 = 3/100= 
3/100 = 3/100 = around 0.03
0.03 ft   The answer is 0.03.
Answer: D
If four coins are tossed, the probability of getting two heads and two tails is ? Choose the correct answer
A) 3/8 B) 3/5 C) 3/9 D) 3/1 E) 3/2

Solution: Since four coins are tossed, sample space = 24   Getting two heads and two tails can happen in six ways.   n(E) = six ways   p(E) = 6/24 = 3/8   3/8nswer: 3/8
Answer: A
A mathematics teacher tabulated the marks secured by 35 students of 8th class. The average of their marks was 72. If the marks secured by Reema was written as 36 instead of 66 then find the correct average marks up to two decimal places.  Pick
A) 72.85  B) 74.31  C) 72.43  D) 73.43  E) Cannot be determined

Solution: Total marks = 35 x 72 =2520   Corrected total marks = 2520 - 36 + 66= 
2520 - 36 + 66 = 2_550
2550   Correct 72.85verage= 2550/35 = 72.85   72.85nswer : 72.85
Answer: A
A circle graph shows how the MegaTech corporation allocates its Research and Development budget: 10% microphotonics; 24% home electronics; 15% food additives; 29% genetically modified microorganisms; 8% industrial lubricants; and the remainder for basic astrophysics. If the arc of each sector of the graph is proportional to the percentage of the budget it represents, how many degrees of the circle are used to represent basic astrophysics research? Select: A) 8° B) 10° C) 18° D) 36° E) 50°

Solution: Here all percentage when summed we need to get 100% . As per data  10+24+15+29+8= 
 10+24+15+29+8 = 86
86%.   So remaining 14% is the balance for the astrophysics.   Since this is a circle all percentage must be equal to 360 degrees.   100% ---- 360 degrees   Then 14% will be 50 degrees..   IMO option 50°.
Answer: E
Find the area of a parallelogram with base 24 cm and height 16 cm? Choose the correct answer
A) 287 cm2	B) 384 cm2	C) 187 cm2	D) 167 cm2	E) 158 cm2

Solution: Area of a parallelogram   = base * height   = 24 * 16= 
24 * 16 = 384
384 cm2   Answer: 384 cm2
Answer: B
The cost of type 1 rice is Rs 15 per Kg and type 2 rice
is Rs 20 per Kg. If both type1 and type 2 are mixed in the
ratio of 2:3,then the price per Kg of the mixed variety
of rice is?	Choices.
A) 15	B) 18	C) 20	D) 25	E) 30

Solution: Let the price of the mixed variety be Rs x per Kg.   Cost of 1 Kg of type 1 rice Rs 15 Cost of 1 Kg of type 2 rice Rs 20   Mean Price Rs x   20-x x-15   (20-x) /( x-15) = 2/3   => 60-3x = 2x-30   5x = 90=>x=18.   ANSWER 18
Answer: B
The total age of A and B is 12 years more than the total age of B and C.C is how many years younger than A ?  Answers:
A) 12
B) 24
C) C is elder than A
D) Data inadequate
E) None of these

Solution: Solution   (A+B)-(B + C)= 12 ⇔ A-C =12. 12nswer 12
Answer: A
At present, the ratio between the ages of Arun and Deepak is 4:5. After 6 years, Arun's age will be 26 years. What is the age of Deepak at present?	Choices:	A) 17 years	B) 15 years	C) 18 years	D) 12 years	E) 25 years

Solution: Let the present ages of Arun and Deepak be 4x and 5x years respectively.   Then, 4x + 6 = 26 => x   = 5   Deepak's age   = 5x   = 25 years.   Answer:25 years
Answer: E
If a sample of data has mean of 20 and SD of 3, which of the following values is more than 2.3 SDs from the mean? Choose the correct choice from the following choices:  A) 16  B) 13  C) 15  D) 18  E) 19

Solution: 2.3 SD's mean is equal to: +/- 2.3*3 = +/- 6.9   ie. 13.1 to 26.9   Answer is: 13
Answer: B
To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of bucket is reduced to two-fifth of its present ?	Choose one
A) 52.5 B) 62.5 C) 72.5 D) 82.5 E) 81.5

Solution: Explanation:   Let the capacity of 1 bucket = x.   Then, capacity of tank = 25x.   New capacity of bucket = 2/5 x.   Required no of buckets = 25x / (2x /5) = 62.5   ANSWER IS 62.525  / (2  /5)= 
25  / (2  /5) = 125/2 = around 62.5
62.5   ANSWER IS 62.5
Answer: B
A man can row a boat at 15 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 60 km downstream?
Answers:
A) 30/16 hours B) 80/13 hours C) 30/73 hours D) 30/13 hours E) 20/7 hours

Solution: Speed downstream = 15 + 6= 
15 + 6 = 21
21 kmph.   Time required to cover 60 km downstream= d/s = 60/21   = 20/7 hours.   Answer:20/7 hours
Answer: E
Can you find the missing number in the sequence below
14 -20 34 -54 ? -144	Choices: A) 88 B) 77 C) 66 D) 55 E) 44

Solution: Solution:   88   Explanation:   14 -20 34 -54 ? -144   The number is difference between right number and left number.   i.e   example     14-(-20)= 
  14-(-20) = 34
34   -20-(34)= -54   34-(-54)= 
34-(-54) = 88
88 answer   -54-(88)= -143   88nswer 88
Answer: A
A man can row downstream at 18 kmph and upstream at 8 kmph. Find the speed of the man in still water and the speed of stream respectively? Answers
A) 3  B) 5  C) 6  D) 4  E) 9

Solution: Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.   Given x + y = 18 --- (1)   and x - y = 8 --- (2)   From (1) & (2) 2x = 26 => x = 13, y = 5. Answer: 5
Answer: B
In February Wilson’s earnings were 40 percent of his family’s total income. In March Wilson earned 25 percent less than in February. If the rest of his family’s income was the same in both months, then, in March, Wilson’s earnings were approximately what percent Z of his family’s total income? Choose the correct choice from the following options:
A) 15%  B) 17%  C) 24%  D) 30%  E) 33%

Solution: Lets suppose the Total Family income in Feb = 100x   Wilson's earning in Feb = 40% of 100x = 40x   33%arnings of remaining family in Feb = 100x - 40x = 60x   Wilson's earning in March 100  - 40= 
100  - 40 = 60
60x   Wilson's earning in March= 75% of Wilson's Feb earnings = 75% of 40x = 30x   33%arnings of remaining family in March = 33%arnings of remaining family in Feb = 60x   Thus Wilson's earning as % of Total family income in March Z= 30x/ (30+60)x = 30x/90x = 33.33%   Thus Answer is 33%
Answer: E
In filling a fish tank with water that is 50 m * 10 m * 1 m the volumes of water filled will be?
Choose the correct choice from the following answers:
A) 500 cu.m  B) 5000 cu.m  C) 50000 cu.m  D) 3000 cu.m  E) 4000 cu.m

Solution: 50 * 10 * 1= 
50 * 10 * 1 = 500
500   500 cu.mNSWER:500 cu.m
Answer: A
If a1 = 1 and an+1= 2an + 5, n = 1, 2 .. , then a10 is equal to ?	Choose the most appropriate option: A) a. 6*2^9 -5 B) b. 5*2^99+6 C) c. 6*2^99+5 D) d. 6*2^99-5 E) e. 6*2^99-6

Solution: Here is solution:   an+1=2an+5............(1)   lets ADD 5 to both sides....   so (an+1) + 5= 2 (an+5)....................taking 2 as common factor   now a1=1. so for n=1, an+5=6.......   putting n=1. we get both sides as,   a2 + 5= 2 * 6 ..............as ( an+5=6 .......(for n=1)..)   a2= 2 *6 - 5   a2= 2 * 2 *3 - 5   a2= 2^2 *3 - 5................. so with same progression   a10= 2^10 * 3 - 5   a10=2* 2^9 * 3 - 5   a10= 6 * 2^9 - 5   a. 6*2^9 -5
Answer: A
5 identical snow plows can clear an iced parking lot in 18 hours. How long would it take 6 such snow plows to clear the same parking lot? Choose one:
A) 1 hour, 15 minutes
B) 2 hours, 30 minutes
C) 3 hours
D) 7 hours, 30 minutes
E) 15 hourss

Solution: 6/5 as many plows will take 5/6 as many hours --> 18*5/6=15 hours.   Answer: 15 hourss.--  18*5/6= 
--  18*5/6 = 15
15 hours.   Answer: 15 hourss.
Answer: E
if v is a positive integer greater than 8, which of the following must be divisible by 4? Choose the correct choice from the following choices:
A) v(v-1)(v+2)(v+3)  B) v(v-1)(v+3)(v+4)  C) v(v-3)(v+2)(v+4)  D) v(v-3)(v+2)(v+3)  E) v(v+1)(v+3)(v+4)

Solution: D.   For any integer v, D is the only answer choice which will always be divisible by 4.   A product of 4 consecutive integers will always be divisible by 4. Since, none of the answer choices are a product of 4 consecutive integers, we have to ensure at least one of the integers is always a multiple of 4. The best way to do that is to ensure the answer choice isv* [(v-1)OR(v+3)] * [(v-2)OR(v+2)] * [(v-3)OR(v+1)]. (ANSWER v(v-3)(v+2)(v+3))
Answer: D
If a bank account has $1000 with an interest rate of 5% compounded annually, how much money will the account have after 10 years? Choose the most appropriate option:
A) 1629
B) 1723
C) 1834
D) 1912
E) 2012

Solution: 1000*1.05^10=1000*1.629= 
1000*1.629 = 1_629
1629   The answer is 1629.
Answer: A
Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 16 cm Choose the correct choice from the following: A) 304 cm2 B) 179 cm2 C) 285 cm2 D) 167 cm2 E) 197 cm2

Solution: 304 cm2rea of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)   = 1/2 (20 + 18) * (16)   = 304 cm2   304 cm2nswer: 304 cm2
Answer: A
A man engaged a servant on the condition that he would pay him Rs.800 and a uniform after one year service. He served only for 9 months and received uniform and Rs.400, find the price of the uniform? Choose the correct option: A) s.800 B) s.85 C) s.90 D) s.100 E) s.120

Solution: 9/12 = 3/4 * 800= 
3/4 * 800 = 600
600   400   -------------   200   1/4 -------- 200   1 --------- ?=> Rs.800   s.800NSWER:s.800
Answer: A
Two identical cubes if one of them is painted pink on its 4 sides and blue on the remaining two side then how many faces painted pink to other cube so that probability of getting the same color is 1/3 when we roll both the cubes.  Choose the most appropriate option.
A) 3	B) 0	C) 8	D) 7	E) 1

Solution: Explanation:   First cube has got 4 pink sides and 2 black sides.   Let the other cube got x sides pink and (6 - x) sides black.   Now when we roll both the dice, we can either pink on both cubes or black on both cubes.   Probability = 46×x6+26×6−x6=1346×x6+26×6−x6=13   =4x+12−2x36=13=4x+12−2x36=13   ⇒x=0⇒x=0   So second cube should not have any pink faces at all.   Answer:0
Answer: B
The ratio of two cow A,B milk is 5:3.3kg milk of cow A get distributed and 1kg milk of cow B get distributed.now,8kg milk of cow B left.Now what is the ratio of cow A and B left milk?	Select
A) 3:2 B) 4:3 C) 5:4 D) 6:5 E) 5:3

Solution: left milk of cow B=3x-1=8,3x=9,x=3.   left milk of cow A=15-3= 
15-3 = 12
12   12/8=3:2.   answer 3:2
Answer: A
The number which exceeds 16% of it by 105 is : Choose the correct choice.
A) 125	B) 52	C) 58	D) 60	E) 62

Solution: Solution   Solution   Let the number be x.   x-16% of x =105   x-16/100x =105   x-4/25x=105   21/25x=105   x=(105x25/21)=125 125nswer 125
Answer: A
A student divided a number by 2/3 when he required to multiply by 3/2. Calculate the percentage of error in his result.
Choices
A) 0  B) 16  C) 18  D) 1  E) 120

Solution: suppose the no is 100   first condition if it mistakenly divided the no by 2/3 ==>100/(2/3)==>150   second condition the no should multiply by 3/2 ==> 100*3/2 ==> 150   hence output should be 150 and mistakenly the output is 150   so pecentage error is zero   0NSWER:0
Answer: A
A popular website requires users to create a password consisting of the digits {1,2,3,4,5,6}. If no digit may be repeated and each password must be at least 5 digits long, how many passwords are possible?	Choose the correct choice:	A) 5! + 6!	B) 2 x 6!	C) 5! x 6!	D) 11!	E) 12!

Solution: If we choose the 6 different digits then they can be arranged in 6! ways.   The number of possible 5-digit passwords is 6*5*4*3*2 = 6!   The total number of passwords is 6! + 6! = 2*6!   The answer is 2 x 6!.
Answer: B
If x = (y)(y + 1) and y is a prime number less than 7, which of the following could not be the product of 2 consecutive integers?
Choose the correct choice from the following answers:
A) a) 5x  B) b) 11x  C) c) 13x  D) d) 30x  E) e) 57x

Solution: Given y is a prime number less than 7   possible values of y are 2 3 5   given, x=y*(y+1)   if y = 2 x=2*3= 
2*3 = 6
6   if y= 3 x=3*4= 
3*4 = 12
12   if y= 5 x=5*6= 
5*6 = 30
30   so possible values of x are 6,12,30   So from options   A. 5x can be (5*6)   B. 11x can be (11*12)   C. 13x can be (13*12)   D. 30x can be (30*31)   E. 57x cannot be   So answer option e) 57x
Answer: E
The average age of three boys is 15 years and their ages are in proportion 3:5:7. What is the age in years of the youngest boy?  Answers.
A) 9 B) 10 C) 11 D) 12 E) 13

Solution: Explanation:   3x + 5x + 7x = 45   x =3   3x = 9   9)
Answer: A
Joe drives 240 miles at 60 miles per hour, and then he drives the next 120 miles at 40 miles per hour. What is his average speed for the entire trip in miles per hour?	Pick one.
A) 42	B) 51	C) 50	D) 54	E) 56

Solution: t1= 240/60= 
240/60 = 4
4 hours   t2=120/40= 
120/40 = 3
3 hours   T=t1+t2=7 hours   Avg speed = Total Distance/T   = 360/7 = 51mph=51
Answer: B
In a shop 50% of the articles are sold at a profit of 20% and the remaining at a loss of 30%.what is the overall profit/loss?  Choose the most appropriate option.
A) 15% profit  B) 8% loss  C) no profit, no loss  D) 20% profit  E) 5% loss

Solution: 50*1.2+50*0.7/100=0.95   ANSW5% lossR:5% loss
Answer: E