MU-NLPC/Calc-aqua_rat huggingface dataset:
If -0.5 < x < 0, which of the following must be true?
I. x^7 < x^2
II. x^3 < 1 – x^3
III. x^4 < x^2	Choose the most appropriate option.
A) I only B) I and II only C) II and III only D) I and III only E) I, II and III

Solution: I. x^7 < x^2 --> from -0.5 < x < 0 it follows that LHS<0<rhs, --="" 1="" <="" ii.="" is="" so="" statement="" this="" true.="" x^3="" –=""> x^3(1+1) < 1 --> negative*positive < 0 < 1, so this statement is also true.   III. x^6 < x^2 --> reduce by x^2 (we can safely do that since from -1 < x < 0 is follows that x^4>0): x^4 < 1. Again, as -1 < x < 0, then x^4 must be less than 1. Hence, this statement is also true.   Answer: I, II and III.</rhs,>
Answer: E
An aeroplane covers a certain distance at a speed of 1500 kmph in 2 hours. To cover the same distance in 1 2/3 hours, it must travel at a speed of:	Answers
A) 2200 kmph  B) 1800 kmph  C) 1900 kmph  D) 2100 kmph  E) none

Solution: Explanation: Distance = (1500 x 2) = 3000 km.   Speed = Distance/Time   Speed = 3000/(5/3) km/hr. [We can write 1 2/3 hours as 5/3 hours]   Required speed = 3000 x 3/5 km/hr = 1800 km/hr.   Answer: Option 1800 kmph
Answer: B
The total weight of six people of equal weights inside a car is 12% of the total weight of the car (inclusive of the six people inside). If three people get down from the car, what will be the ratio of the weight of people inside the car to the weight of the empty car?  Choices
A) 44 B) 45 C) 46 D) 47 E) 48

Solution: Ans. Assume total weight of the car along with people is 100kgs.   Then Total weight of 6 people is 12% of 100 = 12 kgs. So empty car weight = 88 kgs   That is, the weight of a single person = 12/6= 
12/6 = 2
2 kgs.   If three people get down from the car, then there is a six kgs reduction in the total weight and the weight of the remaining people is only 6 kgs.   The required ratio= 6 : 88 = 3 : 44   44nswer 44
Answer: A
If the cost price of 12 pens is equal to the selling price of 7 pens, the gain percent is:  Choose the correct choice from the following choices
A) 80%	B) 90%	C) 71%	D) 40%	E) 10%

Solution: Explanation:   Let C.P. of each pen be Re. 1.   Then, C.P. of 7 pens = Rs. 7; S.P. of 7 pens = Rs. 12.   Gain % = 5/7 * 100 = 71%   Answer:71%
Answer: C
The sum of the two numbers is 15 and their product is 35. What is the sum of the reciprocals of these numbers? Choose the correct choice from the following choices:
A) 15/35	B) 1/35	C) 35/8	D) 7/32	E) None of these

Solution: Let the numbers be a and b. Then, a+b=15 and ab =35.   a+b/ab=15/35; (1/b+1/a)=15/35   Sum of reciprocals of given numbers=15/35.   Correct Option: 15/35
Answer: A
Of the 645 speckled trout in a certain fishery that contains only speckled and rainbow trout, the number of males is 45 more than twice the number of females. If the ratio of female speckled trout to male rainbow trout is 4:3 and the ratio of male rainbow trout to all trout is 3:20, how many female rainbow trout are there?  Choose the correct option:
A) 192 B) 195 C) 200 D) 205 E) 208

Solution: It will be easier if you draw a table for this one. Let T be the total trout.   total speckled trout (ST) = 645   If female speckled trout = fST   then male speckled trout = 45 + 2fST   Therefore 45+ 2fST + fST = 645   We solve and get fST = 200   and mST= 445   Ratio of fST to mRT = 4:3   We have fST = 200   Solve ratio to get mRT = 150   Now ratio of mRT to T = 3:20   We have mRT = 150   Solve ratio to get T = 1000   Now unless youve drawn the table it might get a little complex.   From above we have mST and mRT   mST + mRT = 445 + 150= 
445 + 150 = 595
595   So T - 595= total female trouts   1000 - 595= 
1000 - 595 = 405
405 female trouts   We have from above that fST= 200   So (whew!) fRT = 405 - 200= 
405 - 200 = 205
205 answer is 205
Answer: D
There are 16 bees in the hive , then 7 more fly. How many bees are there in all? Pick:	A) 7	B) 23	C) 12	D) 17	E) 25

Solution: 16+7= 
16+7 = 23
23 . Answer is 23.
Answer: B
Rs.2500 is divided into two parts such that if one part be put out at 5% simple interest and the other at 6%, the yearly annual income may be Rs.140. How much was lent at 5%? Choose the correct answer:
A) Rs.1500
B) Rs.1300
C) Rs.1200
D) Rs.1000
E) Rs.1700

Solution: Explanation:   (x*5*1)/100 + [(2500 - x)*6*1]/100 = 140   X = 1000   ANSWER IS Rs.1000
Answer: D
If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is?	Pick one: A) 1/8 B) 1/2 C) 4/2 D) 1/9 E) 7/2

Solution: The number of exhaustive outcomes is 36.   Let E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then   = 18/36 = 1/2   P(E) = 1 - 1/2 = 1/2.   Answer: 1/2
Answer: B
Two taps A and B can fill a cistern in 12 minutes and 18 minutes respectively. They are turned on at the same time. If the tap A is turned off after 4 minutes, how long will tap B take to fill the rest of the cistern ?	Choices:
A) 8 minute
B) 9 min.
C) 10 min.
D) 7 min.
E) None of these

Solution: In one min, (A + B) fill the cistern = 1⁄12 + 1⁄18 = 5⁄36th   In 4 min, (A + B) fill the cistern = 5⁄36 × 4 = 5⁄9th   Rest part = 1 - 5⁄9 = 4⁄9th   ∵ 1⁄18th part is filled by B in one min.   ∴ 4⁄9th part is filled by B in 18 × 4⁄9 = 8 min   8 minutenswer 8 minute
Answer: A
IF x is an integer greater than 6, then all the following must be divisible by 3 EXCEPT  Choose one:	A) a) 3x^3	B) b)x (x+3)	C) c)9 x^2	D) d)3 x^7	E) e)x(x+1)(x+2)

Solution: *any number multiplied by 3, will be divided by 3   for option b if we put value x=7, 7*10=70 is not divisible by 3   Answer : b)x (x+3)
Answer: B
Jordan passed a point on a track at a constant speed of 50 miles per hour. Then, 15 minutes later, Pauline passed the same point at a constant speed of 60 miles per hour. If both runners maintained their speeds , how long after he passed the gas station did Pauline catch up with Jordan?
Choose one.
A) 30 min B) 45 min C) 1 hr D) 1 hr 15 min E) 1 hr 30 min

Solution: When Pauline is at the point, Jordan is 50/4 miles ahead on the ahead. (the distance covered by him in 15 min)   every hour, pauline runs 10 miles more than Mary. how many hours will it takes him to run 50/4 miles more? the answer is (50/4)/10 = 25/20=1h15min.   Answer 1 hr 15 min
Answer: D
If two girls starting from same point, walking in the opposite directions with 7km/hr and 3km/hr as average speeds respectively. Then the distance between them after 12 hours is?  Choose the correct choice.
A) 120  B) 121  C) 122  D) 123  E) 124

Solution: Explanation:   Total distance = Distance traveled by person 120+ Distance traveled by person B   = (7Ã— 12) + (3Ã— 12)   = 84+ 36= 
84+ 36 = 120
120 Km   120nswer:120
Answer: A
Perimeter of the backwheel is 9 feet and front wheel is 7 feet at a certain distance. The front wheel gets 10 revolutions more than the back wheel. What is the distance?  Choose the correct choice from the following answers:
A) 305
B) 310
C) 315
D) 320
E) 325

Solution: If distance=d   Number of revolutions by back wheel=d/9 & front wheel=d/7   (d/7)-(d/9)=10 ,2d=630 ,d=315   ANSWER:315
Answer: C
You have 59 cubic blocks. What is the minimum number that needs to be taken away in order to construct a solid cube with none left over?  Choose the correct choice from the following answers.
A) 28	B) 29	C) 30	D) 31	E) 32

Solution: Sol.   The next cube number below 64(4 ×4 ×4) is 27(3 ×3 ×3).   In order to construct a solid cube, therefore, with none left over,   59 – 27 = 32 blocks need to be taken away.   Answer : 32
Answer: E
Angelo and Isabella are both salespersons. In any given week, Angelo makes $550 in base salary plus 8 percent of the portion of his sales above $3,000 for that week. Isabella makes 10 percent of her total sales for any given week. For what amount of weekly sales would Angelo and Isabella earn the same amount of money?  Choose the correct choice:
A) 15,500 B) 24,500 C) 25,500 D) 26,500 E) 27,500

Solution: OFFICIAL SOLUTION:   The problem asks for the amount of weekly sales it takes for Angelo and Isabella to earn the same amount of money. You can write an equation that sets Angelo’s and Isabella’s weekly earnings equal to each other, with x representing weekly sales. Weekly earnings for each salesperson equal base salary plus commission. So Angelo’s earnings are 550 + (0.08)(x – 3,000), and Isabella’s are 0.10x. Set up the equation and solve:   550 + (0.08)(x – 3,000) = 0.10x   Distribute the 0.08:   550 + 0.08x – 240 = 0.10x   Combine terms and subtract 0.08x from both sides:   310 = 0.02x   Divide both sides by 0.02:   15,500 = x   Your answer is 15,500.
Answer: A
In a kilometer race, A beats B by 16 meters or 10 seconds. What time does A take to complete the race?	Choose the correct choice from the following answers:
A) 167 sec	B) 190 sec	C) 176 sec	D) 716 sec	E) 615 sec

Solution: Time taken by B run 1000 meters   = (1000 * 10)/16= 
(1000 * 10)/16 = 625
625 sec.   Time taken by A= 625 - 10= 
625 - 10 = 615
615 sec.   Answer:615 sec
Answer: E
John was thrice as old as Tom 6 yrs back. He will be 5/3 times as old as Tom 6 years hence. How old is Tom today?  Pick:
A) 10
B) 11
C) 12
D) 16
E) 21

Solution: Sol. RMBflSk -6 = 3 (Ravi - 6) ...(j)   and Rupesh + 6 = | (Ravi + 6) ...(ii)   Solving both the equations we get,   Ravi = 12 years.   12
Answer: C
A car covers a distance of 624 km in 6 ½ hours. Find its speed?
Choose the correct choice from the following answers: A) 104 kmph B) 776 kmph C) 886 kmph D) 887 kmph E) 665 kmph

Solution: 624/6= 
624/6 = 104
104 kmph   104 kmphnswer: 104 kmph
Answer: A
The area of one square is x^2 + 4x + 4and the area of another square is 4x^2 − 12x + 9. If the sum of the perimeters of both squares is 32, what is the value of x?  Choose the correct choice from the following choices
A) 0
B) 2
C) 2.5
D) 4.67
E) 3

Solution: spotting the pattern of equations both are in form of (X+C)^2 so   A1= (x+2)^2A2= (2x-3)^2   L1= x+2L2= 2x-3   P1 = 4( x+2)P2=4(2x-3)   P1+P2=32   4( x+2) +4(2x-3)=32..............> X=3   Answer: 3
Answer: E
If (8x)/(11y/z -1) = 3x then which of the following is true?
Choose the most appropriate option
A) z = -3y B) z = -y C) z = -x D) z = 3y E) z = 3x

Solution: (8x)/(11y/z - 1) = 3x   => 8z/(11y - z) = 3   => 8z = 33y - 3z   => 11z = 33y   => z = 3y   Hence Ans is z = 3y
Answer: D
Which of the following could be the sides of an obtuse angled triangle? all values are degree only
I. 51, 29, 100
II. 32, 33,4 4
III. 52, 53, 55	Choose the correct choice from the following choices: A) I and III only B) I only C) III only D) I and II only E) I, II and III

Solution: obtuse angled triangle means one angle more than 90deg and total 180 deg.. I   HENCE, (I only)
Answer: B
Excluding stoppages, the speed of a bus is 5454 kmph and including stoppages, it is 4545kmph. For how many minutes does the bus stop per hour?  Choose the correct choice:
A) 12 B) 11 C) 10 D) 9 E) 8

Solution: Explanation:   Speed of the bus excluding stoppages =54=54 kmph   Speed of the bus including stoppages =45=45 kmph   Loss in speed when including stoppages =54âˆ’45=9 kmph=54âˆ’45=9 kmph   â‡’â‡’ In 11 hour, bus covers 99 km less due to stoppages.   Hence, time in which the bus stops per hour   = Time taken to cover 99 km   =distancespeed=954 hour=16 hour =distancespeed=954 hour=16 hour =606 min=10 min   ANSWER IS 10
Answer: C
For a certain set of numbers, if x is in the set, then x - 3 is also in the set. If the number 4 is in the set , which of the following must also be in the set ?
a) 4
b) 1
c) -5  Choose the correct choice from the following
A) a only,  B) b only,  C) c only,  D) a and b only  E) b and c only

Solution: Notice that the question asks which of the following MUST be in the set, not COULD be in the set.   Since 1 is in the set, then so must be   4-3= 
  4-3 = 1
1. Similarly, since 1 is in the set, then so must be 1-3=-2. Could 4 and -1 be in the set? Certainly, but we don't know that for sure.   Answer: B.   Regarding your question: we don't know which is the source integer in the set, if it's 1, then 4 won't be in the set but if the source integer is say 7, then 4 will be in the set. So, 4 may or may not be in the set.
Answer: B
5^100 is divided by 18. Then what is the remainder?
Choose the correct option
A) 11
B) 14
C) 13
D) 16
E) 17

Solution: Here N = 18=2×32   ϕ(18)=18(1−12)(1−13) = 6   So 56 when divided by 18, remainder is 1.   So we can write the given expression 5100=(56)16×54 = (1)16×54 = 52×52=7×7=49   Now 49 when divided by 18, remainder is 13.   13
Answer: C
If two letters are chosen at random (without replacement) from the word EQUAL, what is the probability that none of the letters are vowels? Pick one.
A) 1/5 B) 2/5 C) 1/10 D) 3/10 E) 3/20

Solution: The number of ways to choose two letters is 5C2 = 10   The number of ways to choose two consonants is 2C2 = 1.   P(no vowels) = 1/10   The answer is 1/10.
Answer: C
If nn is a positive integer and (n+1)(n+3)(n+1)(n+3) is odd, then (n+2)(n+4)(n+2)(n+4) must be a multiple of which one of the following?  Select the correct option.
A) 3  B) 4  C) 5  D) 8  E) 10

Solution: (n+1)(n+3)(n+1)(n+3) is odd only when both (n+1)(n+1) and (n+3)(n+3) are odd. This is possible only when nn is even.   Hence, n=2mn=2m, where mm is a positive integer. Then,   (n+2)(n+4)=(2m+2)(2m+4)=2(m+1)2(m+2)=4(m+1)(m+2)(n+2)(n+4)=(2m+2)(2m+4)=2(m+1)2(m+2)=4(m+1)(m+2)   =4 * (product of two consecutive positive integers, one which must be even)=4 * (product of two consecutive positive integers, one which must be even) =4 * (an even number), and this equals a number that is at least a multiple of 8=4 * (an even number), and this equals a number that is at least a multiple of 8   Hence, the answer is (8).
Answer: D
In how many ways can a five-letter password be chosen, using the letters A, B, C, D, E, F, G, and/or H such that at least one letter is repeated within the password?	Pick one: A) 720 B) 864 C) 900 D) 936 E) 26048

Solution: Total number of four letter passwords = 8*8*8*8*8= 
8*8*8*8*8 = 32_768
32768 ------(1)   Total number of passwords in which no letter repeats= 8C5*5!= 56*120= 
56*120 = 6_720
6720------(2)   therefore required value= (1)-(2)= 32768-6720= 
32768-6720 = 26_048
26048   26048
Answer: E
A car covers 4 successive 3km stretches at speed of 10kmph, 20kmph, 30kmph & 60kmph resp. Its average speed is	Choices
A) 20 km/h
B) 25 km/h
C) 30 km/h
D) 35 km/h
E) 45 km/h

Solution: 20 km/hverage speed = total distance / total time   total distance = 4 * 3= 
4 * 3 = 12
12 km   total time= 3/10 + 3/20 + 3/30 + 3/60   = 36/60 hr   speed =12/36 * 60= 
12/36 * 60 = 20
20 kmph   20 km/hnswer : 20 km/h.
Answer: A
A reading list for a certain course consists of 10 books, of which 4 are poems and the rest are novels. Each student is required to read a selection of 4 books from the list, including at most 2 novels. How many selections of 4 books satisfy the requirements?
Choices: A) 90 B) 115 C) 130 D) 144 E) 195

Solution: Case 1 PPNN 2 Poems out of 4 and 2 Novels out of 6 i.e. 4C2 * 6C2 = 90   or   Case 2 PPPN 3 Poems out of 4 and 1 Novels out of 6 i.e 4C3 * 6C1 = 24   or   Case 3 PPPP 4 Poems out of 4 i.e. 4C4 =1   Total no. of selections case 1 + case 2+ case 3 = 90 + 24 +1= 
90 + 24 +1 = 115
115   So answer must be B. 115   ANSWER:115
Answer: B
The sum an integer N and its reciprocal is equal to 78/15. What is the value of N?  Options
A) 3 B) 4 C) 5 D) 6 E) 7

Solution: Write equation in N as follows   N + 1/N = 78/15   Multiply all terms by N, obtain a quadratic equation and solve to obtain N = 5.   correct answer 5
Answer: C
An accurate clock shows 5 o'clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 11 o'clock in the morning? Choose the correct choice from the following answers:
A) 140º	B) 160º	C) 180º	D) 200º	E) 210º

Solution: Angle traced by the hour hand in 6=(360x12)x6º = 180º.   answer :180º
Answer: C
How many 5 digit numbers can be formed which are divisible by 3 using the numerals 0, 1, 2, 3, 4, 5 (WITHOUT REPETITION) Choose the correct choice:
A) 216 B) 3152 C) 240 D) 600 E) 305

Solution: Divisibility rule for 3: Sum of all digits is a multiple of 3   Selections for the above to be valid   1,2,3,4,5   No of possible ways = 5! = 120   0,1,2,4,5   No of possible ways = 4*4! = 96   Total = 120+96= 
120+96 = 216
216   216NS:216
Answer: A
Monica planned her birthday party. She prepared 5 muffins for each of her guests and kept aside two additional muffins in case someone will want extra. After the party, it turned out that one of the guests didn't come but every one of the guests that did come ate six muffins and 3 muffins remained. How many guests did Monica plan on?
Choose one.
A) 3.  B) 4.  C) 5.  D) 6.  E) 7.

Solution: Let x be the number of guests.   Number of muffins prepared = 5x + 2   Number of muffins eaten + Number of muffins remaining = Number of muffins prepared   6(x - 1) + 3 = 5x + 2   6x - 3 = 5x + 2   x = 5   Answer: 5.
Answer: C
Two pipes P and Q can fill a cistern in 10 and 15 minutes respectively. Both are opened together, but at the end of 3 minutes the first is turned off. How much longer will the cistern take to fill? Choose the correct choice from the following choices.
A) 1/2  B) 1/4  C) 2/4  D) 1/4  E) 1/4

Solution: 3/10 + x/15   = 1   x= 10 1/2   1/2nswer: 1/2
Answer: A
In a marketing survey, 60 people were asked to rank three flavors of ice cream, chocolate, vanilla, and strawberry, in order of their preference. All 60 people responded, and no two flavors were ranked equally by any of the people surveyed. If 3/5 of the people ranked vanilla last, 1/10 of them ranked vanilla before chocolate, and 1/3 of them ranked vanilla before strawberry, how many people ranked vanilla first?  Choose the correct choice from the following:  A) 2 people  B) 6  C) 14  D) 16  E) 24

Solution: FIRST OFFUnderstand what you are trying to find - In this case, you are trying to find how many people rank Vanilla first. For someone to rank Vanilla first, they have to rank them before Chocolate or Strawberry. This should be the very first hint that the correct answer cannot be bigger than  1/10 * 60= 
 1/10 * 60 = 6
6.   So if you are time pressured on the real test, at least you narrowed down the selections to two choices - not bad. But what now?   Solve the easier problem. From 60 people, we are already told that 3/5 of them rank Vanilla last, leaving us with 2/5 of the people not ranking vanilla last - 24 people. So what are those combinations that vanilla are not last?   2 people) C, V, S   B) S, V, C   C) C, S, V (vanilla first)   D) S, C, V (vanilla first)   What are we ultimately hunting for here? The number of people that rank vanilla first:C+D   Now let's represent the given info into three equations   1) 2 people+B+C+D= 24(2/5 of the people do not rank vanilla last)   2) 2 people+C+D = 6(1/10 rank vanilla before chocolate)   3) B+C+D = 20(1/3 rank vanilla before strawberry)   Subtract equation 1 from 2, leaving us with   B = 24 - 6= 
24 - 6 = 18
18   Sub in B into equation 3 and solve for C+D   18 + C + D= 20   C+D = 20 - 18= 
20 - 18 = 2
2   There you go! 2 people out of the 60 ranked Vanilla as first 2 people
Answer: A
Water consists of hydrogen and oxygen, and the approximate ratio, by mass, of hydrogen to oxygen is 2:16. Approximately how many grams of oxygen are there in 135 grams of water?	Select.
A) 16
B) 72
C) 112
D) 120
E) 142

Solution: Since the ratio, by mass, of hydrogen to oxygen is 2:16, then oxygen is 16/(2+16)=8/9 of mass of water.   Therefore there are   135*8/9= 
  135*8/9 = 120
120 grams of oxygen in 135 grams of water.   Answer: 120.
Answer: D
If (x/y)=(7/5), find the value (x^2+y^2)/(x^2-y^2)	Choose the correct choice from the following answers.
A) 37/12  B) 59/11  C) 51/77  D) 41/11  E) None of them

Solution: = (x^2+y^2)/(x^2-y^2) = ( x^2 /y^2+ 1)/ ( x^2 /y^2-1) = [(7/5)^2+1] / [(7/5)^2-1]   = [(49/25)+1] / [(49/25)-1] = 37/12   37/12nswer is 37/12.
Answer: A
A man can row his boat with the stream at 20 km/h and against the stream in 4 km/h. The man's rate is?	Select:
A) 1 kmph  B) 7 kmph  C) 98 kmph  D) 6 kmph  E) 8 kmph

Solution: DS = 20   US = 4   S = ?   S = (20 - 4)/2= 
(20 - 4)/2 = 8
8 kmph   Answer: 8 kmph
Answer: E
The average marks obtained by 120 candidates in a certain examination is 35.Find the total marks.
Choose the correct choice from the following answers:
A) 3800
B) 4500
C) 5200
D) 3400
E) 4200

Solution: Following the above formula, we have the total marks =120*35= 
120*35 = 4_200
4200   Answer is 4200
Answer: E
A no. when divided by the sum of 555 and 445 gives 2times their difference as quotient & 30 as remainder. Find the no. is?	Choose the correct choice
A) 124432
B) 145366
C) 157768
D) 178432
E) 220030

Solution: (555 + 445) * 2 * 110 + 30 = 220000 + 30= 
220000 + 30 = 220_030
220030   220030
Answer: E
A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days A do the work if he is assisted by B and C on every third day?  Answers
A) 11 days
B) 15 days
C) 17 days
D) 18 days
E) 19 days

Solution: A's 2 day's work = (1/20 * 2) = 1/10   (A + B + C)'s 1 day work = (1/20 + 1/30 + 1/60) = 1/10   Work done in 3 days = (1/10 + 1/10) = 1/5   Now, 1/5 work is done in 3 days.   Whole work will be done in (3 * 5)= 
(3 * 5) = 15
15 days.   Answer: 15 days
Answer: B
If 1535/1038 = a+1/[b+1/{c+(d+1/e)}]. Find a*b*c*d*e?	Choose the correct choice
A) 165/2	B) 175/2	C) 178/3	D) 187 by 2	E) 197/2

Solution: by expanding 1535/1038 make form like a+1/[b+1/{c+(d+1/e)}   =1+(497/1038) now a=1   =1+{1/(1038/497)}   =1+{1/(2+42/497)}   =1+{1/(2+1/(497/42)} now b= 2 similarly expand   c=11 d= 1 e=34/8   finally a*b*b*c*d*e   1*2*11*1*34/8   187/2   ANSWER:187 by 2
Answer: D
A wire in the form of a circle of radius 3.5 m is bent in the form of a rectangule, whose length and breadth are in the ratio of 6 : 5. What is the area of the rectangle? Options:
A) 12 cm2 B) 30 cm2 C) 17 cm2 D) 18 cm2 E) 19 cm2

Solution: The circumference of the circle is equal to the permeter of the rectangle.   Let l = 6x and b = 5x 2(6x + 5x) = 2 * 22/7 * 3.5   => x = 1   Therefore l = 6 cm and b = 5 cm Area of the rectangle   = 6 * 5= 
6 * 5 = 30
30 cm2   Answer:30 cm2
Answer: B
There are 9 women and 7 men in a certain club. If the club is to select a committee of 2 women and 2 men, how many different such committees are possible?  Choose the correct choice from the following choices:
A) 432 B) 580 C) 624 D) 756 E) 860

Solution: 9C2 * 7C2 = 36*21= 
36*21 = 756
756   The answer is 756.
Answer: D
The average of 11 numbers is 10.7. If the average of the first six numbers is 10.5 and that of the last six numbers is 11.4, then the middle number is  Choose the correct option:
A) 13.7
B) 11.5
C) 81.5
D) 11.5
E) 21.5

Solution: Explanation:   Middle numbers = [(10.5 x 6 + 11.4 x 6) - 10.7 x 11] = 11.5.   13.7nswer: 13.7
Answer: A
If w is 40 percent less than x, x is 40 percent less than y, and z is 46 percent less than y, then z is greater than w by what percent of w?
Options: A) 4% B) 18% C) 36% D) 40% E) 50%

Solution: Given   w= 0.6x, x=0.6y, z=0.54y,   substituting, w=2/3 Z----> z= 1.5w   and thus z is 50% greater than w.   50% is the correct answer.
Answer: E
Look at this series: 98, 98, 90, 90, 82, 82, ... What number should come next?	Choices:
A) 74  B) 15  C) 17  D) 19  E) 11

Solution: In this series, each number is repeated, then 8 is subtracted to arrive at the next number.   The next number is 74   74nswer : 74
Answer: A
Warner Limited has 4 Senior Managing Directors and 6 Managing Directors. Each investment banking deal requires the guidance of three managing directors, at least one of which must be a Senior Managing Director. How many possible investment banking deals can Warner Limited possibly provide guidance for?
Select the correct option:
A) 116  B) 136  C) 100  D) 200  E) 295

Solution: P(at least 1 S D) = P(Total) - P(0 Senior Director)   =101003 - 61003   = 100
Answer: C
12 men take 18 days to complete a job whereas 12 women in 18 days can complete 1/2 of the same job. How many days will 10 men and 8 women together take to complete the same job?
Answers:
A) 6 B) 13 1â„2 C) 15 3/7 D) Data inadequate E) None of these

Solution: 12 M Ã— 18 = 12 W Ã— 18 Ã— 2/1   \ w = 1/2 M   10M + 8W = 10M + 8 Ã— 1/2M = 14 M   \14 men can complete the same work   in 12Ã—18/14=15 3/7days   Answer 15 3/7
Answer: C