MU-NLPC/Calc-aqua_rat huggingface dataset:
In how many ways Chief Minister and Minister be elected from a team of 13 members? Choose the correct answer
A) 128  B) 131  C) 132  D) 143  E) 156

Solution: To do this, if captain is elected first, then we have 13 ways of doing this.   For election of vice-captain, we have only 12 ways left, coz 1 way is already consumed. (Situations like this is called dependent situation. One selection depends upon other selection.)   So, the ans is 13*12= 
13*12 = 156
156 ways.   Answer : 156
Answer: E
Howmany three digits odd numbers can be formed using the digits 4,5,6,7,8,9 (repetition of digits allowed)  Select:  A) 801  B) 106  C) 216  D) 108  E) 116

Solution: There are 3 ways of filling the unit place of the number. The remaining ten's and 100's place canbe filled in 6 ways each. Required number of numbers =3x6x6=108. Ans: 108
Answer: D
The side of a rhombus is 20 m and length of one of its diagonals is 16 m. The area of the rhombus is?	Choose the correct choice from the following answers
A) 223.28	B) 293.28	C) 293.78	D) 291.28	E) 193.28

Solution: area of the rhombus = 1/2 * p * √4(a)2 - (p)2   a= 20 ; p = 16   A=1/2 * 16 *√4(20)2 - (16)2   =1/2 * 16 *√1600 - 256   =1/2 * 16 *√1344   A =293.28   Answer : 293.28
Answer: B
A certain high school has 500 students. Of these students, 20 are taking music, 20 are taking art, and 10 are taking both music and art. How many students are taking neither music nor art?
Choose the correct choice:
A) 430	B) 440	C) 450	D) 460	E) 470

Solution: We're given a series of facts to work with:   1) A certain high school has 500 students.   2) Of these students:   X are taking music,   Y are taking art, and   Z are taking BOTH music and art.   We're asked how many students are taking NEITHER music nor art?   Let's TEST   X = 20   Y = 20   Z = 10   So, we have 20 students taking music, 20 taking art and 10 taking BOTH music and art. That 10 person has been counted TWICE though (once in the music 'group' and once in the art 'group'), so what we really have is...   10 student taking JUST music   10 student taking JUST art   10 student taking BOTH music and art   Total = 30 students   We're asked for the total number of students who are taking NEITHER Course. That is 5000 - 30 = 470.   470
Answer: E
In a house a hall is 20 m long, 15m wide and 5m high. Its interior has to be covered with mat. What will be the total expenditure if it costs Rs. 60 per square m? Select the correct option.
A) Rs.43000
B) Rs.50000
C) Rs.57000
D) Rs.60000
E) Rs.62000

Solution: Length (l) = 20 m, Breadth (b) = 15 m and Height (h) = 5 m   Total area of the hall to be covered with mat = 2(lb + bh + hl)   = 2(20 * 15 + 15 * 5 + 5 * 20)   =2(300 + 75 + 100)   = 2 * 475= 
2 * 475 = 950
950 sq. m   Total expenditure= 60 * 950   = Rs.57000   Rs.57000
Answer: C
In the xy-plane, a triangle has vertices (0,0), (4,0) and (4,7). If a point (a,b) is selected at random from the triangular region, What is the probability that a-b>0?	Choose the correct choice from the following choices.
A) 4/7 B) 2/3 C) 3/5 D) 3/7 E) 1/2

Solution: The area of the right triangle is (1/2)*4*7= 
(1/2)*4*7 = 14
14.   Only the points (a,b) below the line y=x satisfy a - b > 0.   The part of the triangle which is below the line y=x has an area of (1/2)(4)(4) = 8.   P(a - b > 0) = 8/14 = 4/7   The answer is 4/7.
Answer: A
Given a spinner with four sections of equal size labeled A, B, C, and D, what is the probability of NOT getting an A after spinning the spinner two times?	Choose the correct option:
A) 15/16	B) 9/16	C) 1/2	D) 1/4	E) 1/8

Solution: The probability of NOT getting an A after spinning the spinner two times is 3/4*3/4=9/16 (so getting any of the remaining 3 letters out of 4).   Answer: 9/16.
Answer: B
The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. What is the two-digit number?  Choose the correct choice from the following choices.
A) 60  B) 70  C) 50  D) 20  E) cannot be determined

Solution: Let the ten's digit be x and unit's digit by y   Then, x + y = 15 and x - y = 3 or y - x = 3   Solving x + y = 15 and x - y = 3, we get: x = 9, y = 6   Solving x + y = 15 and y - x = 3, we get: x = 6, y = 9   So, the number is either 96 or 69.   Hence, the number cannot be determined.   ANSWcannot be determinedR cannot be determined
Answer: E
A collection of books went on sale, and 2/3 of them were sold for $2.00 each. If none of the 36 remaining books were sold, what was the total amount received for the books that were sold?	Choose the correct choice from the following answers:
A) $144 B) $135 C) $90 D) $60 E) $54

Solution: Since 2/3 of the books in the collection were sold, 1/3 were not sold. The 36 unsold books represent 1/3 of the total number of books in the collection, and 2/3 of the total number of books equals 2(36) or 72. The total proceeds of the sale was 72($2.00) or $144. The best answer is therefore A.   $144nswer: $144.
Answer: A
A certain fraction has the same ratio to 1/18, as 2/5 does to 2/9. What is this certain fraction?
Choose the correct choice from the following answers:
A) 1/5
B) 1/7
C) 1/10
D) 1/12
E) 1/15

Solution: x / (1/18) = (2/5) / (2/9)   x = 2*9*1 / 18*5*2 = 1/10   The answer is 1/10.
Answer: C
The present worth of a bill due sometime hence is Rs. 1100 and the true discount on the bill is Rs. 110. Find the banker’s discount and the banker’s gain.  Options
A) 120 B) 121 C) 130 D) 151 E) None

Solution: Sol.   T.D. = √P.W. * B.G.   ∴ B.G. = (T.D.)² / T.W. = Rs. [110 * 110 / 1100] = Rs. 11.   ∴ B.D. = (T.D. + B.G.) = Rs. (110 + 11) = Rs. 121.   Answer 121
Answer: B
A, B and C invests Rs.2000, Rs.3000 and Rs.4000 in a business. After one year A removed his money; B and C continued the business for one more year. If the net profit after 2 years be Rs.3200, then A's share in the profit is?
Choose the correct choice from the following.
A) 197
B) 127
C) 189
D) 400
E) 198

Solution: 2*12 : 3*12 : 4*24   1: 3: 4   1/8 * 3200= 
1/8 * 3200 = 400
400   Answer: 400
Answer: D
The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively, is :	Choose the correct choice from the following options.
A) 123 B) 127 C) 235 D) 305 E) None of these

Solution: Solution   Required number = H.C.F. of (1657 - 6) and (2037 - 5)   = H.C.F. of 1651 and 2032 = 127. Answer 127
Answer: B
The average of 11 numbers is 10.4. If the average of first six is 10.5 and that of the last six is 11.4 the sixth number is?
Choose the correct choice from the following
A) 9	B) 9.2	C) 10	D) 11.5	E) 17

Solution: 17xplanation:   1 to 11 = 11 * 10.4= 
11 * 10.4 = 114.4
114.4   1 to 6= 6 * 10.5= 
6 * 10.5 = 63
63   6 to 11= 6 * 11.4= 
6 * 11.4 = 68.4
68.4   63 + 68.4= 
63 + 68.4 = 131.4
131.4 – 114.4= 17   6th number = 17   17
Answer: E
The surface area of a cube is 486 Cm3. Find its volume Choose the correct choice from the following answers.
A) 729	B) 739	C) 759	D) 749	E) 719

Solution: Let each edge of the cube be a Cm.   Then 6 a(power)2 = 486 => a(power)2 = 81 = 9(power)2 => a = 9   Volume = a(power)3 = 9(power)3 Cm(power)3 => 729 Cm(power)3   729nswer is 729.
Answer: A
Including Cara and Dan, there are six members on the board of directors for a company. If the board is to be split up into a four-person subcommittee, what fraction of all the possible subcommittees that include Cara, also include Dan?	Choose the correct answer:	A) 3/5	B) 4/5	C) 3/10	D) 7/10	E) 11/20

Solution: The number of possible subcommittees with Cara is 5C3=10.   The number of possible subcommittees with Cara and Dan is 4C2=6.   The fraction of Cara's subcommittees which include Dan is 6/10=3/5.   The answer is 3/5.
Answer: A
Find the ratio in which rice at Rs. 7.20 a kg be mixed with rice at Rs. 5.70 a kg to produce a mixture worth Rs. 6.30 a kg.  Options.
A) 2:7	B) 2:3	C) 2:0	D) 2:1	E) 2:2

Solution: Explanation:   2:3y the rule of alligation:   Cost of 1 kg rice of 1st kind Cost of 1 kg rice of 2nd kind   {\color{2:3lue} \therefore } Required ratio = 60 : 90 = 2 : 3   Answer: 2:3) 2:3
Answer: B
A man in a train travelling at 25km/hr notices that a train going in the opposite direction passes him in 10 sec.If the length of this train is 110m find its speed . Choose the correct choice from the following choices:
A) 30 km/hr
B) 40 km/hr
C) 50 km/hr
D) 60 km/hr
E) 70 km/hr

Solution: relative speed of trains = 110/10 mtrs/sec = 110*18/(10*5)= 40 km/hr   speed of 2nd train = 110-40= 
110-40 = 70
70 km/hr   ANSW70 km/hrR:70 km/hr
Answer: E
A girl goes to her office for work which is 50 miles. She goes to her office few distance by bicycle and remaining by train. The speed of bicycle is 15 mph and that of train is twice of bicycle. If she spend 20 min. more on bicycle, then total time taken by her from going to office from her home?  Choose the correct answer
A) 1 hr 20 min	B) 2 hr 20 min	C) 2 hr 30 min	D) 2 hr 40 min	E) 2 hr 50 min

Solution: Let time travelled in train is x min then in cycle (x+20) min.   (30/60)x + (15/60)(x + 20) = 50 or x = 60   Total time taken 60 + (60 + 20) = 2 hr 20 min   ANSWER:2 hr 20 min
Answer: B
A man can row upstream at 8km/hr and down stream at 11km/hr find mans rate in still water ?	Select:
A) 9.5km/hr B) 4.5km/hr C) 6.5km/hr D) 3.5km/hr E) 5.5km/hr

Solution: :	given upstream(u) =8km/hr   down stream (v)= 11km/hr rate in still water =1/2(u+v)=1/2(8+11)=9.5km/hr 9.5km/hrnswer is (9.5km/hr):9.5
Answer: A
There are 30 socks in a drawer. 60% of the socks are red and the rest are blue. What is the minimum number of socks that must be taken from the drawer without looking in order to be certain that atleast two blue socks have been chosen? Choose the correct choice from the following options
A) 23  B) 37  C) 97  D) 20  E) 21

Solution: Explanation:   Number of red socks = 30 × 60% = 18   If you draw out 18 socks there's a possibility that all of them are red   If you draw out 19 socks one of them has to be a blue one   And if u draw 20 socks then definitely 2 of them are blue socks   So the answer is 20.   Answer:20
Answer: D
John want to buy a $100 Trouser at the store, but he think it’s too expensive. Finally, it goes on sale for $10. What is the percent decrease?	Choose the correct choice from the following options: A) 90% B) 30% C) 40% D) 70% E) 80%

Solution: The is always the difference between our starting and ending points. In this case, it’s 100 – 10 = 90. The “original” is our starting point; in this case, it’s 100. (90/100)*100 = (0.9)*100= 
(0.9)*100 = 90
90%.   90%
Answer: A
Five drainage pipes, each draining water from a pool at the same constant rate, together can drain a certain pool in 16 days. How many additional pipes, each draining water at the same constant rate, will be needed to drain the pool in 4 days?
Choices:
A) 6	B) 9	C) 10	D) 12	E) 15

Solution: This is an inverse proportional problem......   5 pipes in 16 days; So for 4 days, it will be = 16 x 5 / 4 = 20   So, 20-5 = 15   Answer 15
Answer: E
If two drawers of socks contains five different colored socks in each drawer, and a sock is randomly selected from each drawer, what is the probability of getting a pair of the same colored socks?	Choose the correct choice from the following answers
A) 2/5 B) 1/5 C) 1/6 D) 1/2 E) 4/5

Solution: A pair of matching socks.   First solve for NO matching socks:   1st drawer = any color = 5/5   2nd drawer = not a match to the first = 4/5   (5/5)(4/5) =   (1)(4/5) =   20/25   4/5 is the probability of NO matching socks, so...   1 - 4/5 = 1/5 = the probability of getting at least one matching pair of socks.   Answer: 1/5
Answer: B
what is the angle between the hands of a clock when time is 8:20?	Choose the most appropriate option.
A) 65deg B) 75deg C) 50deg D) 15deg E) 30deg

Solution: Angle between two hands =   20h - 11/2 m = 20*8 - 20*11/2 = 160 - 110= 
160 - 110 = 50
50deg   ANSWER:50deg
Answer: C
The lettersmove four steps backward to obtain the letters of the next term
?, SIY, OEU, KAQ, GWM, CSI  Options:	A) AAH	B) AHU	C) WMC	D) RTR	E) UGV

Solution: WMC   WMWMC   The lettersmove four steps backward to obtain the letters of the next term
Answer: C
Priya covers journey from kavali to nellore by car at average speed of 70 Km/hr. She returns back by scooty with an average speed of 70 Km/hr. Find her average speed during the whole journey?
Choose the correct choice.
A) 60Km/hr  B) 70Km/hr  C) 80Km/hr  D) 90Km/hr  E) 100km/hr

Solution: Explanation:   Average speed = 2 xy/x+y   = 2*70*70/140= 
2*70*70/140 = 70
70 Km/hr   Answer: Option 70Km/hr
Answer: B
Of the 200 people attending a conference, 60 have signed up for the Marketing workshop and 180 have signed up for the Accounting workshop. If 50 of the people attending did not sign up for either workshop, then the number of people who signed up for both the Marketing and the Accounting workshops is:
Choose the correct option: A) 60 B) 75 C) 80 D) 85 E) 90

Solution: Since the information in the prompt refers to the 'standard' 5 groups, you can use the Overlapping Sets Formula to get to the solution:   Total = Gp.1 + Gp.2 - Both + Neither   200 = 60 + 180 - Both + 50   200 = 290 - Both   Both = 90   Final Answer:   90
Answer: E
Lebron has 297 bottles of beer in his fridge and is inviting eight friends over to drink and watch the game. He wants to make things seem as if everybody will get the same amount of beer. How many beers will he have to drink in order maintain the illusion that he is sharing equally amongst his friends? Pick.
A) 1 B) 4 C) 2 D) 8 E) 0

Solution: Using the divisibility rule of nine, we add the digits of 297 together and get the number 18. 18 is divisible by 9 and our answer is 0 beers(option 0)
Answer: E
By selling an umbrella for Rs. 300, a shop keeper gains 15%. During a clearance sale, the shopkeeper allows a discount of 10% on the marked price. His gain percent during the sale is? Select the correct option: A) 6.5% B) 2% C) 5.88% D) 3% E) 4%

Solution: Marked price = Rs. 300   C.P. = 100/115 * 300 = Rs. 255   Sale price = 90% of Rs. 300 = Rs. 270   Required gain % = 15/255 * 100 =5.88%.   Answer: 5.88%
Answer: C
3 candidates in an election & received 1136, 7636 and 11628 votes respectively. What % of the total votes did the winning candidategot in that election?
Pick.
A) 50%	B) 52%	C) 57%	D) 60%	E) 65%

Solution: Total number of votes polled = (1136 + 7636 + 11628)= 
(1136 + 7636 + 11628) = 20_400
20400   So, Required percentage= 11628/20400 * 100= 
11628/20400 * 100 = 57
57%   57%
Answer: C
Two trains 200 m and 150 m long are running on parallel rails at the rate of 40 kmph and 45 kmph respectively. In how much time will they cross each other, if they are running in the same direction?  Choose the most appropriate option.
A) 72 sec  B) 132 sec  C) 192 sec  D) 252 sec  E) None

Solution: Solution   Relative Speed	= (45 - 40 )= 
(45 - 40 ) = 5
5 kmph=(5 x 5 / 18)m/sec   = (25 / 18 ) m/sec   Time taken	= (350 x 18 / 25) sec   = 252 sec.   Answer 252 sec
Answer: D
At what rate percent on simple interest will Rs.750 amount to Rs.900 in 5 years? Pick
A) 8 B) 7 C) 4 D) 3 E) 2

Solution: 150 = (750*5*R)/100   R = 4%   Answer: 4
Answer: C
10 men, working 3 hours a day can complete a work in 18 days. How many hours a day must 15 men work to complete the work in 12 days ? Pick one:
A) 3 hours a day
B) 5 hours a day
C) 6 hours a day
D) 7 hours a day
E) 8 hours a day

Solution: Explanation:   More Men, Less Hours {Indirect Proportion}   Less Days, More Hours {Indirect Proportion}   [men 15 10   days 12 18] ::3:x   =>xâˆ—15âˆ—12=10âˆ—18âˆ—3   =>x=10âˆ—18âˆ—3/ 15âˆ—12   =>x=3   Option 3 hours a day
Answer: A
Find the smallest number of four digits exactly divisible by 4,5,7 and 8. Choose the correct choice.
A) 1150  B) 1160  C) 1140  D) 1152  E) 1145

Solution: Smallest number of four digits is 1000.   Required number must be divisible by L.C.M. of 4,5,7,8 i.e 280,   On dividing 1000 by 280,we get 120 as remainder.   Therefore, Required number = 1000 +( 280 â€“ 120 ) = 1160.   Answer is 1160.
Answer: B
Two persons start at the same point, walk in opposite directions with 6 km/hr and 7 km/hr respectively.
What is the distance separated after 3 and half hrs? Choose the correct choice from the following answers
A) 45.5 km
B) 27.250 km
C) 28.250 km
D) 29.250 km
E) 25.250 km

Solution: As the two persons are moving in the opposite direction, so they will be separateed in 1 hour = 6 + 7= 
6 + 7 = 13
13 km.   They will be separated in 2.5 hours= 13 * 3.5= 
13 * 3.5 = 45.5
45.5 km   45.5 kmNSWER:45.5 km
Answer: A
3889 + 12.952 – ? = 3854.002	Select
A) 47.095
B) 47.752
C) 47.932
D) 47.95
E) None

Solution: EXPLANATION   Let 3889 + 12.952 – x = 3854.002.   Then x = (3889 + 12.952) – 3854.002   = 3901.952 – 3854.002   = 47.95.   Answer 47.95
Answer: D
Three cards are drawn successively, without replacement from a pack of 52 well shuffled cards.
What is the probability that first two cards are queens and the third card drawn is an ace?	Choose the correct option
A) 2/5525 B) 3/5525 C) 2/5525 D) 2/5526 E) 4/5525

Solution: Let Q denote the event that the card drawn is queen and A be the event that   the card drawn is an ace. Clearly, we have to find P (QQA)   Now P(Q) = 4/52   Also, P (Q|Q) is the probability of second queen with the condition that one queen has   already been drawn. Now there are three queen in (52 - 1)= 
(52 - 1) = 51
51 cards.   Therefore P(Q|Q)= 3/51   P(A|QQ) is the probability of third drawn card to be an ace, with the condition   that two queens have already been drawn. Now there are four aces in left 50 cards.   Therefore P(A|QQ) = 4/50   By multiplication law of probability, we have   P(QQA) = P(Q) P(Q|Q) P(A|QQ)   = 4/52 × 3/51 × 4/50   = 2/5525.   2/5525)
Answer: A
An woman swims downstream 45 km and upstream 25 km taking 5 hours each time; what is the speed of the current?
Pick
A) 2	B) 1	C) 3	D) 4	E) 2.1

Solution: 45 --- 5 DS = 9   ? ---- 1   25---- 5 US = 5   ? ---- 1 S = ?   S = (9 - 5)/2= 
(9 - 5)/2 = 2
2   2nswer: 2
Answer: A
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?
Choices: A) 11 Kmph B) 68 Kmph C) 88 Kmph D) 19 Kmph E) 66 Kmph

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: 68 Kmph
Answer: B
A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 400 m long?  Choose the most appropriate option.
A) 176 Sec B) 190 Sec C) 178 Sec D) 160 Sec E) 276 Sec

Solution: L = S*T   S= 1200/120= 
1200/120 = 10
10 m/Sec.   Total length (160 Sec)= 1600 m   T = 160 Sec/S   T = 1600/10= 
1600/10 = 160
160 Sec   Answer:160 Sec
Answer: D
The average salary of a person for the months of January, February, March and April is Rs.8000 and that for the months February, March, April and May is Rs.8500. If his salary for the month of May is Rs.6500, find his salary for the month of January?
Choose the correct choice from the following.
A) 299	B) 2889	C) 4500	D) 2728	E) 2762

Solution: Sum of the salaries of the person for the months of January, February, March and April = 4 * 8000= 
4 * 8000 = 32_000
32000 ----(1)   Sum of the salaries of the person for the months of February, March, April and May= 4 * 8500= 
4 * 8500 = 34_000
34000 ----(2)   (2)-(1) i.e. May - Jan= 2000   Salary of May is Rs.6500   Salary of January = Rs.4500   Answer: 4500
Answer: C
One computer can upload 100 megabytes worth of data in 5 seconds. Two computers, including this one, working together, can upload 1300 megabytes worth of data in 40 seconds. How long would it take for the second computer, working on its own, to upload 100 megabytes of data?
Choose the correct choice from the following.
A) 6	B) 8	C) 9	D) 11	E) 13

Solution: Since the first computer can upload 100 megabytes worth of data in 5 seconds then in   5*8= 
  5*8 = 40
40 seconds it can upload   8*100= 
  8*100 = 800
800 megabytes worth of data, hence the second computer in 40 seconds uploads   1300-800= 
  1300-800 = 500
500 megabytes worth of data. The second computer can upload 100 megabytes of data in 8 seconds.   Answer: 8.
Answer: B
The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 42 kmph, find the speed of the stream? Choose the correct answer:
A) 65 kmph B) 88 kmph C) 14 kmph D) 66 kmph E) 44 kmph

Solution: The ratio of the times taken is 2:1.   The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1)= 
(2+1)/(2-1) = 3
3/1= 
3/1 = 3
3:1   Speed of the stream= 42/3= 
42/3 = 14
14 kmph..Answer: 14 kmph
Answer: C
The ratio of the present ages of two Friends is 2 : 3 and six years back, the ratio was 1 : 3. What will be the ratio of their ages after 4 years ?
Choose the correct choice from the following choices.
A) 1:4 B) 3:4 C) 1:2 D) 3:1 E) 3:2

Solution: let the ages be 2x,3x   6yrs back,so   2x-6/3x-6=1/3   x=4   after 4 yrs   2x+4,3x+4   2(4)+4,3(4)+4   12:16   3:4   ANSWER:3:4
Answer: B
The price of a furniture is Rs. 3,25,000. It was insured to 85% of its price. The furniture was damaged completely in an incident and the insurance company paid 90% of the insurance. What was the difference between the price of the furniture and the amount received ? Choose the correct answer
A) Rs 36,583 B) Rs 67,375 C) Rs 76,375 D) Rs 76,735 E) None of these

Solution: Explanation :   Amount paid to furniture owner = 90% of 85% of Rs. 3,25,000.   = Rs. (90/100 85/100 325000)   = Rs. 2,48,625.   Required difference = Rs. (325000 - 248625)   = Rs. 76,375.   Answer : Rs 76,375
Answer: C
For which of the following functions f is f(c) = f(1-c) for all c? Select the correct option:
A) f (c) = 1 - c
B) f (c) = 1 - c^2
C) f (c) = c^2 - (1 - c)^2
D) f (c) = c^2*(1 - c)^2
E) f (x) = x/(1 - x)

Solution: I remember seeing this problem in a GMATprep test. I think choice D should be F(c)=(c^2) (1-c)^2. If that is true then substituting (1-c) for will give us the same function back and the answer choice is f (c) = c^2*(1 - c)^2, where the function is multiplicative
Answer: D
The diagonal of a square is twice the side of equilateral triangle then the ratio of Area of the Triangle to the Area of Square is?	Select:  A) 3√9  B) 3√8  C) 3√7  D) 3√5  E) 3√1

Solution: Let the side of equilateral triangle = 1 unit.   We know that area of an equilateral triangle = 3–√4a234a2   As side = 1 unit area of the equilateral triangle = 3–√434   Now Diagonal of the square = 2 (side of the equilateral triangle) = 2   We know that area of the square = 12D212D2 where D = diagonal   So area of the square = 12(22)=212(22)=2   Ratio of the areas of equilateral triangle and square = 3–√434 : 2 ⇒⇒ 3√8   Answer:3√8
Answer: B
Find the greatest number which, while dividing 19, 83 and 67, gives a remainder of 3 in each case?	Select:
A) 16 B) 17 C) 18 D) 19 E) 20

Solution: Subtract the remainder 3 from each of the given numbers: (19-3)= 
(19-3) = 16
16, (67-3)=64 and   (83-3)= 
  (83-3) = 80
80. Now, find the HCF of the results 16, 64 and 80, we get 16. Thus, the greatest number is 16   16NSWER:16
Answer: A
If two dice are thrown together, the probability of getting prime number on both dice is	Select:
A) 5/9	B) 1/9	C) 2/9	D) 4/9	E) 7/9

Solution: The number of exhaustive outcomes is 36.   Let E be the event of getting a prime number on both the dice.   P(E) = 8/36 = 2/9.   2/9)
Answer: C
If r and s are positive integers and r-s=6, which of the following has the greatest value M?  Choose the correct choice from the following options:  A) 2r  B) 2s  C) r +s  D) 2r-s  E) 2s-r

Solution: You can answer this question by using Number Properties and logic or by TESTing VALUES.   We're told that R and S are POSITIVE INTEGERS and that R-S = 6. We're asked which of the 5 answers has the GREATEST value.   IF....   R = 8   S = 2   2rnswer 2r: 2R = 2(8) = 16   2rnswer B: 2S = 2(2) = 4   2rnswer C: R+S = 8+2= 
8+2 = 10
10   2rnswer D: 2R-S= 2(8) - 2 = 14   2rnswer E: 2S-R = 2(2) - 8 = -4   Final 2rnswer:   2r
Answer: A