MU-NLPC/Calc-aqua_rat huggingface dataset:
A and B together can do a piece of work in 6 days and A alone can do it in 11 days. In how many days can B alone can do it? Choose the most appropriate option:
A) 12 days	B) 15 days	C) 66/5 days	D) 21 days	E) 22/5 days

Solution: Explanation:   A and B can do work 1/6 in 1 day   A alone can do 1/11 work in 1 day   B alone can do (1/6 -1/11) =5/66 work in 1 day   => complete work can be done in 66/5 days by B   Answer: Option 66/5 days
Answer: C
A vendor bought bananas at 6 for a rupee. How many for a rupee must he sell to gain 20%?  Choices: A) 2 B) 4 C) 7 D) 5 E) 3

Solution: CP of 6 bananas = 1   Gain = 20%   SP of 6 bananas=1×120/100=12/10   ⇒The number of bananas he should sell for Rs.1 for a gain of 20%=10/12∗6=10/2= 
10/2 = 5
5   ANSWER:5
Answer: D
How many four digit numbers have no repeat digits, do not contain zero, and have a sum of digits H equal to 28?
Choose the most appropriate option.
A) 14	B) 24	C) 28	D) 48	E) 96

Solution: First, look for all 4 digits without repeat that add up to 28. To avoid repetition, start with the highest numbers first.   Start from the largest number possible 9874.   Then the next largest number possible is 9865.   After this, you'll realize no other solution. Clearly the solution needs to start with a 9 (cuz otherwise 8765 is the largest possible, but only equals 26). With a 9, you also need an 8 (cuz otherwise 9765 is the largest possible, but only equals 27). With 98__ only 74 and 65 work.   So you have two solutions. Each can be rearranged in 4!=24 ways. So H=24+24=48.48
Answer: D
If a 10% deposit amounting to $110 has been paid toward buying a brand new TV, how much remains to be paid? Choose the correct option:
A) $880 B) $990 C) $1000 D) $1100 E) $1210

Solution: Explanation:   Let's start with what the total price of the TV would be. If 10% is equal to $110 then 100% equals $x. We just have to multiply $110 by 10 to get total amount=$1100. Out of this amount we then need to deduct the amount already paid which was $110 so we have $1100-$110=$990   Answer: Option $990 1100- 110= 
 1100- 110 = 990
$990   Answer: Option $990
Answer: B
In a class of 52 students, 12 enrolled for both English and German. 22 enrolled for German. If the students of the class enrolled for at least one of the two subjects, then how many students enrolled for only English and not German?  Pick.
A) 30
B) 10
C) 18
D) 28
E) 32

Solution: Total=English+German-Both+Neither --> 52=English+22-12+0 --> English=42 --> Only English=English-Both=42-12= 
42-12 = 30
30   30nswer: 30.
Answer: A
How much is 80% of 40 is greater than 4/5 of 25? Pick.
A) 229	B) 87	C) 26	D) 12	E) 667

Solution: (80/100) * 40 – (4/5) * 25   32 - 20= 
32 - 20 = 12
12   Answer: 12
Answer: D
A man whose bowling average is 12.4, takes 4 wickets for 26 runs and there by decreases his average by 0.4. the number of wickets taken by him before his last match is?  Pick one:
A) 53
B) 54
C) 55
D) 56
E) 57

Solution: 12.4*x+26=(4+x)12   solve equation x=55   ANSWER:55
Answer: C
There are 408 boys and 240 girls in a school which are to be divided into equal sections of either boys or girls alone. Find the total number of sections thus formed.
Pick
A) 27  B) 32  C) 35  D) 30  E) 45

Solution: Explanation:   HCF (408, 240) = 24   The number of boys or girls that can be placed in a section = 24.   Thus the total number of sections is given by   408/24+240/24 =17+10= 
17+10 = 27
27   27nswer: 27
Answer: A
If a man buys 10 lollipops for $90 and sold them for $6 dollars determine his loss. Select the correct option
A) 50  B) 60  C) 70  D) 20  E) 90

Solution: Cost of 10 lollipops = $80   Sold each lollipop for $6   So he sold 10 lollipops for $(10 × 6) = $60   Loss = $(80 – 60) = $20   answer :20   Therefore, loss = $ 20.
Answer: D
The average price of three items of furniture is Rs. 15000. If their prices are in the ratio 3:5:7, the price of the cheapest item is : Choose the correct choice from the following options:  A) 6000  B) 7000  C) 8888  D) 9000  E) None of these

Solution: Explanation:   Let their prices be 3x, 5x and 7x.   Then, 3x + 5x + 7x = (15000 * 3) or x = 3000.   Cost of cheapest item = 3x = Rs. 9000. Answer: 9000
Answer: D
A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place?  Choose the correct answer:
A) 1.99 km	B) 2.88 km	C) 4.49 km	D) 2.99 km	E) 7.88 km

Solution: M = 6   S = 1.2   DS = 6 + 1.2= 
6 + 1.2 = 7.2
7.2   US= 6 - 1.2= 
6 - 1.2 = 4.8
4.8   x/7.2 + x/4.8= 1   x = 2.88   Answer: 2.88 km
Answer: B
A runs times as fast as B. If A gives B a start of 80 m, how far must the winning post be so that A and B might reach it at the same time?	Choose one.
A) 200
B) 378
C) 277
D) 298
E) 797

Solution: Explanation:   Ratio of the speeds of A and B =5 : 1 = 5 :3   Thus, in race of 5 m, A gains 2 m over B.   2 m are gained by A in a race of 5 m.   80 m will be gained by A in race of \inline \fn_jvn {\color{Black} \left ( \frac{5}{2}\times 80 \right )} m =200m   \inline \fn_jvn {\color{Black} \therefore }Winning post is 200 m away from the starting point.   200nswer: 200) 200 m
Answer: A
A is twice as good a work man as B and together they finish the work in 14 days. In how many days A alone can finish the work? Select.
A) 20 B) 21 C) 22 D) 23 E) 24

Solution: Explanation:   WC = 2:1   2x + x = 1/14 => x = 1/42   2x = 1/21   A can do the work in 21 days.   Answer: 21
Answer: B
What is the value of 10^8- 6^4?	Choose one
A) 9,99,98,623  B) 9,99,98,704  C) 9,99,98,800  D) 9,99,99,521  E) 9,99,99,932

Solution: As 10^n will always have last digit as 0 AND 6^n will always as last digit 6.. hence difference of such sum should always be ending with 4 and there is only on option ..   Answer 9,99,98,704
Answer: B
Which of the following is a parallelogram?
Options.
A) 130,50,130,50(angle in deg)
B) 120,30,130,20(angle in deg)
C) 95,95,95,95(angle in deg)
D) a & c
E) none

Solution: sum of adjacent angles is 180 degrees.   130,50,130,50(angle in deg)NSWER:130,50,130,50(angle in deg)
Answer: A
If N is the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case.What is the sum of the digits of N ?	Pick one.
A) 1	B) 2	C) 3	D) 5	E) 4

Solution: N = H.C.F. of (4665 - 1305), (6905 - 4665) and (6905 - 1305)   = H.C.F. of 3360, 2240 and 5600 = 1120.   Sum of digits in N = ( 1 + 1 + 2 + 0 )= 
( 1 + 1 + 2 + 0 ) = 4
4   ANSW4R:4
Answer: E
The cost of producing x tools by a company is given by
C(x) = 2000 x + 5500 (in $)
a) What is the cost of 100 tools?
Choose the correct choice from the following choices:
A) 215500 $	B) 205800 $	C) 125900 $	D) 226500 $	E) 205500 $

Solution: Solution   C(100) = 2000*100 + 5500= 
2000*100 + 5500 = 205_500
205500 $   Answer 205500 $
Answer: E
Each digit in the two-digit number G is halved to form a new two-digit number H. Which of the following could be the sum of G and H
Choose the correct answer
A) 153  B) 150  C) 137  D) 132  E) 89

Solution: let the number be x, now x is halved => x/2..the question asks what is x?   x(number) + x/2 (half of that number) = something   => 3x/2 = something   => x = 2 (something) / 3   so the answer choice must be divisible by 3   eliminate C, E right away   check the rest   D satisfies   3x/ 2 = 132   => x = 88   Verify. 88 + 44 = 132   Answer is 132
Answer: D
What is the next term in the below series.
1/5 , 1/2 , 1/3 , 2/5 ,1, 2/3, 3/5, 1 1/2 ,1, 4/5,?	Options:
A) 1/5
B) 0
C) 2
D) 2/5
E) 3/5

Solution: 1/5 2/5 3/5 4/5   1/2 1 1 1/2 ?   1/3 2/3 1 4/3   ans :2   ANSWER:2
Answer: C
The price of an item changed from $120 to $100. Then later the price decreased again from $100 to $80. Which of the two decreases was larger in percentage term? Choose the correct option.
A) 10%	B) 20%	C) 30%	D) 40%	E) 50%

Solution: First decrease in percent   part / whole = (120 - 100) / 120 = 0.17 = 17%   Second decrease in percent   part / whole = (100 - 80) / 100= 
(100 - 80) / 100 = 1/5 = around 0.2
0.20= 20%   The second decrease was larger in percent term. The part were the same in both cases but the whole was smaller in the second decrease.   Answer 20%
Answer: B
The distance traveled by eagle in one year approximately 150,000,000 miles.The distance traveled by eagle in 50 years?  Choose the correct option:
A) 10<8>
B) 10<16>
C) 10<4>
D) 10<12>
E) 10<11>

Solution: The distance traveled by eagle in one year = 150,000,000 miles.   The distance traveled by eagle in 50 years = 150,000,000 miles * 50 years = 7,500,000,000 miles   (ie) 75*10<8> exponent 10<8>nswer : 10<8>
Answer: A
A committee of 5 people is to be selected from 8 people. How many different committees are possible? Choices:  A) 28  B) 40  C) 56  D) 168  E) 336

Solution: Because the order does not matter in selecting 5 people for the committee, this is a combination question.   The number of ways to select 5 people from 8 = 8C5 = 8!/5!*3! = 56. Hence 56.
Answer: C
In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr? Choose the correct choice from the following answers
A) 2.5
B) 3
C) 4
D) 5
E) 6

Solution: Speed = 144 * 5/18= 
144 * 5/18 = 40
40 m/sec   Time taken= 100/40= 
100/40 = 5/2 = around 2.5
2.5 sec.   2.5nswer: Option 2.5
Answer: A
The area of the square formed on the diagonal of a rectangle as its side is 108 1/3 % more than the area of the rectangle. If the perimeter of the rectangle is 28 units, find the difference between the sides of the rectangle?  Choose one:  A) 3m  B) 5m  C) 8m  D) 2m  E) 1m

Solution: Let the sides of the rectangle be l and b respectively.   From the given data,   (√l2 + b2) = (1 + 108 1/3 %)lb   => l2 + b2 = (1 + 325/3 * 1/100)lb   = (1 + 13/12)lb   = 25/12 lb   => (l2 + b2)/lb = 25/12   12(l2 + b2) = 25lb   Adding 24lb on both sides   12l2 + 12b2 + 24lb = 49lb   12(l2 + b2 + 2lb) = 49lb   but 2(l + b) = 28 => l + b = 14   12(l + b)2 = 49lb   => 12(14)2 = 49lb   => lb = 48   Since l + b = 14, l = 8 and b = 6   l - b = 8 - 6= 
8 - 6 = 2
2m.   Answer:2m
Answer: D
Three friends James, David and Charlie divide $1230 amongs them in such a way that if $5, $10 and $15 are removed from the sums that James, David and Charlie received respectively, then the share of the sums that they got will be in the ratio of 9: 10 : 11. How much did Charlie receive?
Choose the correct choice from the following options
A) $600
B) $575
C) $550
D) $580
E) $615

Solution: A+B+C = 1230   Given ratio 9:10:11   Let us say the shares of A,B,C deducting 5,10,15 be a,b,c   a+b+c = 1230-30= 
1230-30 = 1_200
1200= 30K   c share = (1200X30)/60 = 600   C = charlie share = 600+15= 
600+15 = 615
615   Option $615
Answer: E
A water tank is three-fifths full. Pipe A can fill a tank in 15 minutes and pipe B can empty it in 6 minutes. If both the pipes are open, how many minutes will it take to empty or fill the tank completely? Pick:  A) 2  B) 4  C) 6  D) 8  E) 10

Solution: The combined rate of filling/emptying the tank = 1/15 - 1/6 = -1/10   Since the rate is negative, the tank will be emptied.   A full tank would take 10 minutes to empty.   Since the tank is only three-fifths full, the time is  (3/5) * 10= 
 (3/5) * 10 = 6
6 minutes   The answer is 6.
Answer: C
The speed of a car increases by 2 kms after every one hour. If the distance travelling in the first one hour was 30 kms. what was the total distance traveled in 12 hours?	Options:
A) 252 kms  B) 152 kms  C) 492 kms  D) 752 kms  E) 152 kms

Solution: Explanation:   Total distance travelled in 12 hours =(30+32+34+.....upto 12 terms)   This is an A.P with first term, a=30, number of terms,   n= 12,d=2.   Required distance = 12/2[2 x 30+{12-1) x 2]   = 6(82)   = 492 kms.   Answer: 492 kms
Answer: C
While driving from A-ville to B-town, Harriet drove at a constant speed of 95 kilometers per hour. Upon arriving in B-town, Harriet immediately turned and drove back to A-ville at a constant speed of 155 kilometers per hour. If the entire trip took 5 hours, how many minutes did it take Harriet to drive from A-ville to B-town?	Choices:
A) 138
B) 148
C) 150
D) 162
E) 186

Solution: 5hr = 300min.   If harriet spend equal hrs on each leg she will spend 150min on each. Since speed A-B is less than speed B-A and distance on each leg is the same, time spent on A-B is more than 150min, which mean we can eliminate ans. A, B and C.   Now let plug in ans. D or E and verify which one give same distance on each leg.   E. t= 186min   * leg A-B ---> d = 95.186/60 = 17670/60   * leg B-A ----> d = 155*114/60 = 17670/60   so the correct ans. is186
Answer: E
A train ,155 meters long travels at a speed of 45 km/hr crosses a bridge in 30 seconds. The length of the bridge is	Choose the correct choice from the following choices:
A) 270 m B) 245 m C) 235 m D) 220 m E) 240 m

Solution: Explanation:   Assume the length of the bridge = x meter   Total distance covered = 155+x meter   total time taken = 30s   speed = Total distance covered /total time taken = (155+x)/30 m/s   => 45 Ã— (10/36) = (155+x)/30   => 45 Ã— 10 Ã— 30 /36 = 155+x   => 45 Ã— 10 Ã— 10 / 12 = 155+x   => 15 Ã— 10 Ã— 10 / 4 = 155+x   => 15 Ã— 25 = 155+x = 375   => x = 375-155= 
375-155 = 220
220   Answer: Option 220 m
Answer: D
There are 7 players in a bowling team with an average weight of 112 Kg. If two new players join the team, one weighs 110 Kg and the second weighs 60 Kg, what will be the new average weight?
Choose the correct choice from the following answers.
A) 115 Kg.
B) 110 Kg.
C) 106 Kg.
D) 105 Kg.
E) 100 Kg.

Solution: The New average will be= (112*7+110+60)/9= 
(112*7+110+60)/9 = 106
106 kgs   106 Kg. is the answer
Answer: C
A can have a piece of work done in 5 days, B can work three times faster than the A, C can work four times faster than A. How many days will they take to do the work together ?	Choose the correct choice from the following.
A) 3 days B) 8/9 days C) 3/2 days D) can't say E) none

Solution: A's 1 day work is 1/12   B's 1 day work is 3/12   3/2 days's 1 day work is 4/12   (A+B+3/2 days)'s 1 day work(1/12+3/12+4/12) is 2/3   so, they can finish the work in 3/2 days   ANSWER:3/2 days
Answer: C
There are 20 people among whom two are sisters. Find the number of ways in which we can arrange them around a circle so that there is exactly one person between the two sisters ?  Choose the correct choice from the following choices.
A) 18!  B) 2! x 19!  C) 19!  D) 17!  E) None of these

Solution: First arrange the two sisters around a circle in such a way that there will be one seat vacant between them. [This can be done in 2! ways since the arrangement is not circular.]   Then, the other 18 people can be arranged on 18 seats in 18! ways.So, total number of ways = 18! x 2! ways   ANSWNone of theseR:None of these
Answer: E
In a camp,there is a meal for 120 men or 200 children.If 180 children have taken the meal,how many men will be catered to with the remaining meal ?  Answers
A) 20  B) 30  C) 12  D) 50  E) 60

Solution: Solution   There is a metal for 200 children. 180 children have taken the meal.   Remaining meal is to be catered to 20 children.   Now, 200 children = 120 men   20 children =( 120/200x20)men= 12 men. Answer 12
Answer: C
A fires 5 shots to B's 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 27 times, A has killed:	Options
A) 10 B) 20 C) 30 D) 40 E) 50

Solution: Let the total number of shots be x. Then,   Shots fired by A = 5/8x   Shots fired by B = 3/8x   Killing shots by A = 1/3 of 5/8x = 5/24x   Shots missed by B = 1/2 of 3/8x = 3/16x   Therefore, 3x/16 = 27 or x = (27 x 16/3)= 144.   Birds killed by A = 5x/24 = (5/24 x 144)= 30.   Answer is 30.
Answer: C
A shopkeeper professes to sell his goods at cost price but uses a weight of 800 gm instead of kilogram weight.Thus, he makes a profit of
Choose the correct choice from the following choices.
A) 20%
B) 22%
C) 25%
D) None of these
E) Cannot be determined

Solution: Solution   Therefore,Profit	=(200/800×100)%   = 25%.   Answer 25%
Answer: C
A baker makes chocolate cookies and peanut cookies. His recipes allow him to make chocolate cookie in batches of 7 and peanut cookies in batches of 6. If he makes exactly 99 cookies, what is the minimum number of chocolate chip cookies he makes?  Answers:	A) 7	B) 14	C) 21	D) 28	E) 35

Solution: 7C+6P=99   We need to maximize P to minimize C so that the eq is also satisfied   Try substitution for CP to solve so that eqn is satisfied   The least value of C for which equation gets satisfied is 5   i.e. 7*3+6*13=21+78= 
21+78 = 99
99   Hence 21 is the answer
Answer: C
You are renting an apartment and you need √784 for each side, how many feet are you looking to measure?
Select:
A) 21
B) 22
C) 23
D) 24
E) 28

Solution: Try filling the numbers into the answer y x y =   Find the closest to 784.   Answer 28
Answer: E
A farmer spent $35 on feed for chickens and goats. He spent 40% money on chicken feed, which he bought at a 10% discount off the full price, and spent the rest on goat feed, which he bought at full price. If the farmer had paid full price for both the chicken feed and the goat feed, what amount would he have spent on the chicken feed and goat feed combined?	Choose the most appropriate option:
A) $36.55	B) $38.50	C) $39.20	D) $39.50	E) $40.60

Solution: A farmer spent 40% money on chicken feed, so he spent 0.4*$35=$14 on chicken feed, thus he spent the remaining 35-14 0.4* 35= 
 0.4* 35 = 14
$14 on chicken feed, thus he spent the remaining   35-14= 
  35-14 = 21
$21 on goat feed.   Now, since he bought chicken feed at a 20% discount then the original price of it was x*0.9=$14 --> x=$15.55.   Therefore if the farmer had paid full price for both the chicken feed and the goat feed, then he would he have spent 15.55+21=$36.55.   $36.55nswer: $36.55.
Answer: A
If -2/(a - 6) = 4/(a + 4), then a = ?  Choices:
A) 2/3 B) 1/2 C) 5/3 D) 8/3 E) 7/3

Solution: Multiply all terms of the given equation by (a - 6)(a + 4), simplify and solve   (a - 6)(a + 4)[ -2/(a - 6) ] = (a - 6)(a + 4) [ 4/(a + 4) ]   - 2 (a + 4) = 4 (a - 6)   a = 8/3   correct answer 8/3
Answer: D
A cube of sides 9 is first painted red and then cut into smaller cubes of side 3. How many of the smaller cube have painted on exactly 2 sides?	Choose the correct answer.
A) 30  B) 24  C) 12  D) 8  E) 9

Solution: n=side of big cube/side of small cube   and no. Of smaller cubes with two surfaces painted is (n-2)*12   (3-2)*12= 
(3-2)*12 = 12
12 ans   ANSWER:12
Answer: C
25 binders can bind 1400 books in 21 days. How many binders will be required to bind 1600 books in 20 days?  Choose the correct choice from the following options
A) 87 B) 18 C) 17 D) 16 E) 30

Solution: Binders Books Days   25 1400 21   x 1600 20   x/25 = (1600/1400) * (21/20) => x = 30   Answer:30
Answer: E
Given that E and F are events such that P(E) = 10 P(F) = 2 and P(E n F) = 10,
find P (E|F) and P(F|E) Choose one
A) 1	B) 69	C) 24	D) 5	E) 12

Solution: Here, E and F are events   P(E|F) = P(EnF)/P(F) = 10/10= 
10/10 = 1
1   P(F|E)= P(EnF)/P(E) = 10/2= 
10/2 = 5
5.   5)
Answer: D
A sum was put a simple interest at a certain rate for 7 years. Had it been put at 2% higher rate, it would have fetched Rs. 350 more. The sum is:
Choose the correct option:
A) s.500
B) s.1000
C) s.1500
D) s.2000
E) s.2500

Solution: Explanation :   Let the sub be Rs.x and the initial rate be R%.Then   x Ã— (R+2) Ã— 7/100âˆ’xÃ—RÃ—7/100=350   â‡’x Ã— 2Ã—7/100=350   â‡’x Ã— 7 /100=175   â‡’7x=17500   â‡’x=2500   s.500nswer : Option s.500
Answer: A
Assuming i have an infinite supply of coins.
What is the fewest number of coins would be required in order to make sure each and every coin touched exactly three other coins.  Choose the correct choice:
A) 3 B) 7 C) 4 D) 8 E) 2

Solution: 4   4   Three placed flat on the table in a triangle(touching each other) and put the fourth one on top of them in the middle.
Answer: C
Birbal is a witty trader who trade of a mystical fruit grown far in north. He travels from one place to another with three sacks which can hold 30 fruits each. None of the sack can hold more than 30 fruits. On his way, he has to pass through thirty check points and at each check point, he has to give one fruit for each sack to the authorities.
How many mystical fruits remain after he goes through all the thirty check points?  Pick.
A) 25  B) 26  C) 27  D) 28  E) 29

Solution: Solution:   25 Fruits   Remember we told you that Birbal is a witty trader. So his sole motive is to get rid of the sacks as fast as he can.   For the first sack:   He must be able to fill fruits from one sack to other two sacks. Assume that he is able to do that after M check points. Now to find M,   (Space in first sack) M + (Space in second sack) M = (Remaining fruits in Third Sack) 30 – M   M = 10   Thus after 10 checkpoints, Birbal will be left with only 2 sacks containing 30 fruits each.   Now he must get rid of the second sack.   For that, he must fill the fruits from second sack to the first sack. Assume that he manages to do that after N checkpoints.   (Space in First Sack) N = (Remaining fruits in second sack) 30 – N   N = 15   Thus after he has crossed 25 checkpoints, he will be left be one sack with 30 fruits in it. He has to pass five more checkpoints where he will have to give five fruits and he will be left with twenty five fruits once he has crossed all thirty check points.   25nswer 25
Answer: A
25% of 30% of 45% is equal to? Choose the most appropriate option:  A) 0.03375  B) 0.03372  C) 0.03379  D) 0.03372  E) 0.03328

Solution: (25/100) * (30/100) * (45/100)   1/4 * 3/10 * 9/20   27/800= 
27/800 = 27/800 = around 0.03375
0.03375   0.03375nswer: 0.03375
Answer: A
Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?
Answers:
A) 2  B) 6  C) 5  D) 4  E) 8

Solution: Explanation:   Explanation:   Let rate = R% and time = R years.   Then,   Answer: 6) 6
Answer: B
The average age of students of a class is 15.8 years. The average age of boys in the class is 16.4 years and that of the girls is 15.1 years, The ratio of the number of boys to the number of girls in the class is Select the correct option:
A) 7 : 6	B) 2 : 3	C) 9 : 3	D) 6 : 3	E) 2 : 5

Solution: Explanation:   Let the ratio be k : 1. Then,   k * 16.4 + 1 * 15.1 = (k + 1) * 15.8   <=> (16.4 - 15.8) k = (15.8 - 15.1) <=> k = 0.7/0.6 = 7/6.   Required ratio = 7/6 : 1 = 7 : 6.   7 : 6nswer: 7 : 6
Answer: A
A small table has a length of 12 inches and a breadth of b inches. Cubes are placed on the surface of the table so as to cover the entire surface. The maximum side of such cubes is found to be 4 inches. Also, a few such tables are arranged to form a square. The minimum length of side possible for such a square is 24 inches. Find b.
Choices:  A) 8  B) 16  C) 24  D) 32  E) 48

Solution: From the info that the maximum sides of the cubes is 4, we know that the GCF of 12 (=2^2*3) andbis 4 (=2^2), sob=2^x, where x>=2.   From the second premise, we know that the LCM of 12 (2^2*3) andbis 24 (2^3*3), sob=2^3 or 2^3*3 (8 or 24).   Combining 2 premises shows the answer is 8(8).
Answer: A
Two trains leave a station traveling the same direction. Train A leaves the station traveling at a constant speed of 60 mph, and train B leaves the station traveling at a constant speed of 80 mph. If both trains maintain constant speeds, in how many minutes will train B overtake train A if train A left 40 minutes prior to train B?  Options:
A) 90  B) 100  C) 110  D) 120  E) 130

Solution: We can use 120=RT [distance=rate*time]   Train A will have traveled for 40 minutes longer than train B when B overtakes A, so   time of train A: T+40minutes = T+(2/3) hours (use hours since the rate is in hours)   time of train B: T   rate of train A: 60 mph   rate of train B: 80 mph   the distances traveled by each will be equal when train B overtakes train A, so we can set the right sides of 120=RT equal for the two trains   (rate of train A)*(time of train A) = (rate of train B)*(time of train B)   60*(T+2/3)=80*T   60T + 40 = 80T   40 = 20T   2 = T   2 hours = 120 minutes   120
Answer: D