MU-NLPC/Calc-aqua_rat huggingface dataset:
If the product of the integers w, x, y and z is 840, and if 1 < w < x < y < z, what is the value of w + z? Choose the correct choice from the following options:
A) 10
B) 11
C) 16
D) 18
E) 21

Solution: 840= 4* 5 * 6* 7   So w = 4, x = 5, y = 6, z = 7   w + z = 4+ 7= 
4+ 7 = 11
11   Answer - 11
Answer: B
In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 44, the dividend is:
Choices:
A) 4884	B) 5340	C) 5342	D) 5345	E) 5356

Solution: Divisor = (5 * 44)= 
(5 * 44) = 220
220= 10 * Quotient = Divisor   => Quotient = 220/10= 
220/10 = 22
22   Dividend= (Divisor * Quotient) + Remainder   Dividend = (220 * 22) + 44= 
(220 * 22) + 44 = 4_884
4884.   4884
Answer: A
Bullock likes to keep a spare tyre in his car every time. On a certain day, he travels 1, 20,000 km and just to make the most of all the tyres, he changes the tyres between his journey such that each tyre runs the same distance.
What is the distance traveled by each tyre?
Choices:	A) 70,000	B) 60,000	C) 80,000	D) 96,000	E) 10,000

Solution: The distance traveled by each tyre:   4/5 * 1, 20, 000km = 96,000 km. 96,000
Answer: D
If a person walks at 20 km/hr instead of 10 km/hr, he would have walked 40 km more. The actual distance traveled by him is?
Select:
A) 40 km
B) 76 km
C) 18 km
D) 16 km
E) 97 km

Solution: Let the actual distance traveled be x km. Then,   x/10 = (x + 40)/20   10x - 400 =>x = 40 km.   40 kmnswer: 40 km
Answer: A
If a man lost 10% by selling oranges at the rate of 10 a rupee at how many a rupee must he sell them to gain 50%? Pick one: A) 6 B) 8 C) 7 D) 4 E) 2

Solution: 90% ---- 10   150% ---- ?     90/150* 10= 
  90/150* 10 = 6
6   6nswer: 6
Answer: A
Marge has 3 pumps for filling her swimming pool. When all 3 pumps work at their maximum rates, the swimming pool is filled in 56 minutes. Pump 1's maximum rate is twice the maximum rate of pump 2 and four times the maximum rate of pump 3. How long would it take Marge to fill the pool if she used only pump 2 at its maximum rate ?
Choose the correct choice:
A) 3hrs, 16mins
B) 6hrs, 32mins
C) 7hrs, 12mins
D) 13hrs, 4mins
E) 14hrs, 24mins

Solution: The rate of pump 1 = 4x job/minute.   The rate of pump 2 = 2x job/minute.   The rate of pump 3 = x job/minute.   Given that x+2x+4x=1/56 --> x=1/392 --> (time) = (reciprocal of rate) = 392 minutes x/2= 196 = 3 hrs 16 minutes.   3hrs, 16minsnswer: 3hrs, 16mins
Answer: A
A watch which gains uniformly, is 6 min. slow at 8 o'clock in the morning Sunday and it is 6 min. 48 sec. fast at 8 p.m. on following Sunday. When was it correct? Choices
A) 20 min past 7 pm on Tuesday  B) 20 min. past 7 p.m.on Wednesday  C) 20 min. past 7 p.m. on Thursday  D) 20 min. past 7 p.m. on Friday  E) None of these

Solution: Explanation :   Time from 8 a.m. on Sunday to 8 p.m. on following Sunday = 7 days 12 hours = 180 hours   The watch gains (5 + 29/5) min. or 54/5 min. in 180 hrs.   Now 54/5 min. are gained in 180 hrs.   5 min. are gained in (180 x 5/54 x 5) hrs = 83 hrs 20 min. = 3 days 11 hrs 20 min.   Watch is correct 3 days 11 hrs 20 min. after 8 a.m. of Sunday.   It will be correct at 20 min. past 7 p.m. on Wednesday.   Answer : 20 min. past 7 p.m.on Wednesday
Answer: B
At a certain stage of a soccer tournament, the score ratio of teams A, B and C was 3:4:5. Eventually, the score ratio of A to B has doubled while the score ratio of A to C has halved. If the final score of team C was 40, what was the final score Q of team B?	Choose the correct choice:
A) 1)8	B) 2)10	C) 3)20	D) 4)40	E) 5)80

Solution: A to B = 3 : 4   So, on doubling we get 6 : 4   A to C = 3 : 5   So, on halving we get 1.5 : 5 or 3 : 10 or 6 : 20   So final ratio = 6 : 4 : 20.   If 20x = 40   4x = 8   Hence, answer is 1)8
Answer: A
If a bus moving at the speed of y km/hr travels a distance of x km, which of the following cannot be equal to the distance traveled?  Options:
A) y-x km B) y/2 km C) (y-x)/2 km D) x/y km E) x-y km

Solution: This question can be solved by TESTing VALUES, but there's a particular pattern that you have to recognize to make the workeasy.   We're not really limited by anything in this question, so X and Y can be anything. Under normal circumstances, I won't TEST the number 1 in PS questions (as it often leads to duplicate answers), but here it's a great option (since we're looking to eliminate 4 answers, multiple TESTs are going to be likely anyway).   We're given information on speed (y km/hour) and distance (x km). We're asked which of the 5 answer choices CANNOT be the distance traveled.   IF....   Y = 2 and X = 1   Answers A (2-1 = 1) and B (2/2 = 1) are POSSIBLE. Eliminate A and B.   IF....   Y = 3 and X = 1   Answer C ([3-1]/2 = 1) is POSSIBLE. Eliminate C.   IF....   Y = 1 and X = 1   Answer D (1/1 = 1) is POSSIBLE. Eliminate D.   Final Answer:   x-y km
Answer: E
What is the measure of the radius of the circle that circumscribes a triangle whose sides measure 9, 40 and 41?  Answers
A) 6 B) 4 C) 24.5 D) 20.5 E) 12.5

Solution: Explanatory Answer   9, 40 and 41 is Pythagorean triplet. So, the triangle is right angled.   Key property about right triangles   In a right angled triangle, the radius of the circle that circumscribes the triangle is half the hypotenuse.   In the given triangle, the hypotenuse = 41.   Therefore, the radius of the circle that circumscribes the triangle = 41/2= 
41/2 = 41/2 = around 20.5
20.5 units.   Choice 20.5
Answer: D
When is |x-7| = 7-x?
Pick one
A) x>7  B) x<7  C) x=7  D) x<0  E) x<=7

Solution: When is |x-7| = 7-x?   Choice A: X=7, it is true but X cannot be always 7   Choice B: X=0, it is also true, but X cannot be always 0   Choice C: X>7, it is false, for e.g. X=6, then one side of equation is 2 and the other side is -2   Choice D: X<=7, this choice encapsulate Choice A, Choice B and for all other conditions and is true for above said equation. Hence the answer choice is x<=7.
Answer: E
A machine, working at a constant rate, manufactures 72 staplers in 28 minutes. How many staplers does it make in 1 hr 52 min?	Choose the correct answer:
A) 268	B) 262	C) 300	D) 288	E) 250

Solution: Change 1 hr 52 min to 112 min. For this, we need to set up a simple proportion of staplers per time 72/28= S/112.   The absolutely worst thing you could do at this point in the problem is to cross-multiply. That would be a supremely unstrategic move. We can cancel the common factor of 28 in the two denominators.   72/28*28 = S/112*28   72/1 = S/4   S = 4* 72= 
4* 72 = 288
288   The machine would be 288 staplers in 1 hr 52 min.   Answer:288
Answer: D
Virat buys an old car for Rs. 50000 and spends Rs. 2000 on its repairs. If he sells the car for Rs. 62000, his gain percent is:	Pick.
A) 19.23% B) 11 (1/9) % C) 12.1 % D) 12% E) None of these

Solution: Explanation:   C.P. = Rs. (50000 + 2000) = Rs. 52000   S.P. = Rs. 62000.   Gain% = ( (10000 / 52000) * 100 ) % = 19.23%   19.23%NSWER 19.23%
Answer: A
If a, r, and c are consecutive even integers and a < r < c, all of the following must be divisible by 4 EXCEPT  Answers.
A) a + c  B) r + c  C) ac  D) (bc)/2  E) (abc)/4

Solution: I did get the correct answer within 80 seconds and it was not by luck either. I did not pick numbers but just used the concept stated by Ian.   The 3 numbers can be written as   a, (a + 2)(a + 4).   If 'a' is divisible by 4, then even 'c' or 'a + 4' is divisible by 4. However, is 'b' is divisible by 4, then both 'a' and 'a + 4' are still divisible by 2.   A - (a + c) = a + (a + 4) = 2a + 4 = 2(a + 2) = 2b. 2b will always be divisible by 4 even if 'b' is not divisible by 4. Reason: 'b' already has a prime factorization of at least a '2'. Hence '2b' has two 2s.   C - ac = a(a+4). If, as stated above, one of them is divisible by 4, then the product is divisible. If both of them are not divisible by 4, then the product is still divisible by 4 because of the presence of two 2s again in the prime factorization.   D - bc/2 = (a + 2)(a + 4)/2. Either b or c is divisible by 2. Hence, if we assume that b is divisible by 2 and not divisible by 4, then it leaves us just one possibility. Is c divisible by 4? It has to be because c is the next consecutive even integer.   E - abc/4 = a(a + 2)(a + 4)/4. One of these integers is divisible by 4 already. If we again assume 'b' to be that integer divisible by 4, then we are left with the question - Is a(a + 4) divisible by 4? This is the same as option C.   B - r + c = (a + 2) + (a + 4) = 2a + 6 = 2(a + 3). (a + 3) will never be divisible by 2 because it is an odd integer. Hence, 2(a + 3), although divisible by 2, will not be divisible by 4 because it has just one 2 in its prime factorization.   As a whole, whether you choose numbers (2, 46 being the easiest) or solve conceptually, the answer is still easily obtainable within 2 minutes.r + c
Answer: B
An investor bought 200 shares of stock in ABCD company in 1990. By 1992, the investment was worth only 2/3 of its original value. By 1995, the 200 shares were worth only 2/5 of their value in 1990. By what percent did the value of the investment drop from 1992 to 1995? Select the correct option
A) 16 2/3%	B) 25%	C) 40%	D) 50%	E) 66 2/3%

Solution: Let price of each share in 1990 = X.   Total cost in 1990 = 200X   Now Price in 1992 = 2/3 * 200X = 400/3 * X   Now price in 1995 = 2/5 *200= 
2/5 *200 = 80
80X   %40%hange in 1995 from 1992= [(400/3* X -80X) / (400/3 *X) ] *100 = 40%   Answer 40%
Answer: C
In a group of 6 boys&4 girls a Committee of 4 persons is to be formed. In how many different ways can it be done so that the committee has at least 1girl? Choose the correct choice from the following options.
A) 110	B) 130	C) 145	D) 195	E) 200

Solution: The committee of 4 persons is to be so formed that it has at least 1 woman The different ways that we can choose to form such a committee are:   (i) lw. 3 m in t 6X5X4' x 6C3 = 4x — — 80 3X2X1   x 6c2 =42:: x 26:: = 90 (ii) 2w. 2 m in °C2 (iii) 3w. 1 m in 4C3 x 6C1 = 4 x 6 = 24 (iv) 4w in 6C4 = 1 Total no. of different ways in which a committee of 4 persons can be formed so that it has at least one woman. = 80 + 90 + 24 + 1= 
80 + 90 + 24 + 1 = 195
195   195
Answer: D
What are the number of ways to select 3 men and 2 women such that one man and one woman are always selected?  Choose the correct choice from the following options: A) 26 ways B) 19 ways C) 30 ways D) 76 ways E) 15 ways

Solution: The number of ways to select three men and two women such that one man and one woman are always selected = Number of ways selecting two men and one woman from men and five women   = ⁴C₂ * ⁵C₁ = (4 * 3)/(2 * 1) * 5= 
(4 * 3)/(2 * 1) * 5 = 30
30 ways.   Answer: 30 ways
Answer: C
we have two cubes which are joined to each other covering one face of each. and remaining faces of both are colored with the different colors.then the first cube is cut into 8 smaller cubes and another in 27 smaller cubes. what is the total number of faces having no color?	Choose one
A) 141 B) 142 C) 143 D) 144 E) 145

Solution: each cube having 6 faces   for each cube 5 faces has color and one face for each has not   1st cube divided into 8 smaller cubes so num of faces = 8*6= 
8*6 = 48
48   in this 48 faces  5*4= 
 5*4 = 20
20 faces having the color and 28 don't   because if we divided a cube into 2^n smaller cubes (2^3= 8) then each face of original cube is divided into 2^(n-1) smaller faces (2^2 = 4) [and inner faces also there]   similarly 2nd cube divided into 27 smaller cubes so num of faces = 27*6= 
27*6 = 162
162   in tiis 162 faces  5*9= 
 5*9 = 45
45 faces having color and 117 don't   total no of faces having no color= 28+117= 
28+117 = 145
145   ANSW145R:145
Answer: E
A cistern 6m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is: Choose one:
A) 49 m2
B) 50 m2
C) 53.5 m2
D) 55 m2
E) 58 m2

Solution: Area of the wet surface	= [2(lb + bh + lh) - lb]   = 2(bh + lh) + lb   = [2 (4 x 1.25 + 6 x 1.25) + 6 x 4] m2   = 49 m2. 49 m2nswer: Option 49 m2
Answer: A
HCF of two numbers is 11 and the product of these numbers is 363, what is the the greater number? Pick one.
A) 28	B) 31	C) 33	D) 35	E) 38

Solution: The numbers be 11a and 11b   11a × 11b = 363   ab = 3   co-primes with product 3 are (1, 3)   Hence the numbers with H33F 11 and product 363   = (11 × 1, 11 × 3)   = (11, 33)   Numbers are 11 and 33   The greater number = 33
Answer: C
Sony and Johnny caught 25 fishes. Sony caught four times as many as Johnny. How many fishes did Johnny catch?	Pick
A) 5 B) 16 C) 34 D) 38 E) 42

Solution: s+j=25   s=4*j   j=5   5NSWER:5
Answer: A
Which of the following is closer to (21!+20!)/(21!-20!)?
Choose the correct choice from the following choices.
A) 49	B) 36	C) 25	D) 16	E) 1

Solution: Notice that 21! = (21)(20!), so we can factor out 20! from top and bottom.   (21!+20!)/(21!-20!)=[20!(21+1)]/[20!(21-1)]   = (21+1)/(20-1)   = 22/19   ≈ 1   Answer: 1
Answer: E
If integers ending in zero are excluded, what is the unit digit of the product of the even integers from 802 to 898, inclusive?  Choose the most appropriate option:
A) 14  B) 12  C) 10  D) 6  E) 8

Solution: 802 x 804 x 806 x 808 => unit digit 4   812 x 814 x 816 x 818 => unit digit 4   892 x 894 x 896 x 898 => unit digit 4   So we have 10 numbers ending by 4 to multiply.   Given that 4 x 4 = 16, we have 5 numbers ending by 6 to multiply   Given that 6 x 6 = 36, we have 3 numbers ending by 6 to multiply   So the unit digit is 6   Answer : 6
Answer: D
Three 6 faced dice are thrown together. The probability that no two dice show the same number on them is ?
Choices:
A) 5/8	B) 5/9	C) 5/2	D) 5/1	E) 5/6

Solution: No two dice show same number would mean all the three faces should show different numbers. The first can fall in any one of the six ways. The second die can show a different number in five ways. The third should show a number that is different from the first and second. This can happen in four ways.   Thus   6 * 5 * 4= 
  6 * 5 * 4 = 120
120 favourable cases.   The total cases are   6 * 6 * 6= 
  6 * 6 * 6 = 216
216.   The probability= 120/216 = 5/9.   Answer: 5/9
Answer: B
It is given that 2^32 + 1 is exactly divisible by a certain number. Which one of the following is also divisible by the same number W?	Options:
A) a. 2^96 + 1
B) b. 2^16 - 1
C) c. 2^16 + 1
D) d. 7 * 2^33
E) e. 2^64 + 1

Solution: a³ + b³ =(a+b)(a² -ab +b²)   Now, let (2^32 + 1) be (a+b)   a³ + b³ = (2^96 + 1)   Now, as mentioned in formula above,   a³ + b³ is always divisible by (a+b)   So any factor of W (a+b) is a factor of (a³ + b³)   Henca a. 2^96 + 1
Answer: A
There are 20 students with an average height of 105 cms in a class. Then 10 students with an average height of 120 cms join the class. What will be the average height of the class now?	Choose one
A) 110 cms  B) 120 cms  C) 100 cms  D) 115 cms  E) 130 cms

Solution: 20 students average height is 105cms   sum of heights/ 20 =105cms   sum of heights of 20 students= 105*20= 
105*20 = 2_100
2100   10 students of average height 120 added   so their, sum of 10 students height / 10= 120   sum of heights of 10 students = 1200cms   By adding heights of 20 and 10 students , 1200+2100 = 3300   average of 30 students = 3300/30= 
3300/30 = 110
110 cms   110 cmsNSWER:110 cms
Answer: A
In how many ways 7 boys and 7 girls can be seated in a row so that boys and girls are alternate? Choose the correct choice from the following:
A) 50803200
B) 50328000
C) 50003280
D) 50703200
E) 50603200

Solution: number of ways = 2*7!*7! = 50803200   50803200nswer is 50803200
Answer: A
√{(1.5)(10^9)} is closest to which of the following? Answers.
A) 5,000 B) 20,000 C) 40,000 D) 100,000 E) 200,000

Solution: √{(1.5)(10^9)} = √{(15)(10^8)} = √(15)√(10^8) = (√15) * 10,000 which is almost 40,000.   The answer is 40,000.
Answer: C
The football association pays $2000 out of $8000 it owes to refrees. Then it pays $6000 out of the $12000 owes for the year to players.
How much did the ratio of payments made to monies owed increase?	Choose the correct choice:	A) A) 75%	B) B)100 %	C) C)1%	D) D) 50%	E) E) 25%

Solution: Ratio in 1st case 2000:8000(1/4)   Ratio in second case 6000/12000 (2/4)   percentage increase is (difference/initial quantity)*100   (1/4)/(2/4 )* 100= 100%   Correct option is 100 %
Answer: B
8 boys complete a work in 14 days . In how many days will 14 boys complete that work?	Choose the correct choice from the following:
A) 14 days  B) 7 days  C) 8 days  D) 6 days  E) 5 days

Solution: Explanation:   1 boy 1 day work = 14 × 8,   14 boys complete the work in 14 × 8/14= 8 days   Answer: Option 8 days
Answer: C
The side of a square is increased by 20% then how much % does its area increases? Choices.
A) 44.00 % B) 45.25 % C) 48.75 % D) 50.00 % E) 40.00 %

Solution: a = 100 a2 = 10000   a = 120 a2 = 14400   ----------------   10000 --------- 4400   100 -------? => 44.00 %   44.00 %nswer:44.00 %
Answer: A
A room of 5m 44cm long and 3m 74cm broad is to be paved with squre tiles. Find the least number of squre tiles required to cover the floor.  Choose the most appropriate option
A) 233 B) 877 C) 279 D) 176 E) 291

Solution: Explanation:   area of the room = 544 * 374 sq cm   size of largest square tile = H.C.F of 544cm and 374cm= 34cm   area of 1 tile = 34*34 sq cm   no. of tiles required = (544*374) / (34 * 34)= 
(544*374) / (34 * 34) = 176
176   Answer: 176) 176
Answer: D
If the price of a commodity is decreased by 20% and its consumption is increased by 20%, what will be the increase or decrease in expenditure on the commodity?	Choose the most appropriate option:
A) 4% increase B) 4% decrease C) 8% increase D) 8% decrease E) None

Solution: Solution: Let the initial expenditure on the commodity be Rs. 100.   Now, the price decreases by 20%,   Current Price = (100 - 20% of 100) = Rs. 80.   Same time due to decrement in price 20% consumption has been increased. So,   Current expenses on commodity = (80 + 20% of 80)= Rs. 96.   Here, the initial expenditure was Rs. 100 which became 96 at the end, it means there is 4% decrement in the expenditure of the commodity.   Mind Calculation Method:   100===20%↓(Decrement in Price)===>80===20%↑(Increment in Consumption)===>96.   Thus, there is a decrement of 4%.   Answer: Option 4% decrease
Answer: B
What is the present worth of Rs. 122 due in 2 years at 5% simple interest per annum?	Choose the correct option
A) Rs.154.32	B) Rs.121.42	C) Rs. 112	D) Rs.110.99	E) Rs.120.99

Solution: Let the present worth be Rs. x. Then,   S.I. = (122 - x)   (x * 5 * 2) / 100 = (122 - x)   10x = 12200 - 100x   110x = 12200 => x = 110.99   ANSWER:Rs.110.99
Answer: D
For any positive integer p, the sum of the first p positive integers equals p(p+1)/2 . If q and p are positive integers and q > p, what is the sum of all the integers between q and p, inclusive? Select the correct option
A) q(q+1)/2 + p(p+1)/2
B) q(q+1)/2 - p(p-1)/2
C) q(q+1)/2 - p(p+1)/2
D) q(q+1)/2 + p(p-1)/2
E) q(p+1)/2 - p(q-1)/2

Solution: The sum of all the integers between q and p,inclusiveis the sum of the first q positive integersminusthe sum of the first p-1 positive integers.   The sum of the first q positive integers is q(q+1)/2;   The sum of the first p-1 positive integers is (p-1)p/2;   Therefore the answer is q(q+1)/2 - (p-1)p/2.   Answer: q(q+1)/2 - p(p-1)/2.
Answer: B
The average age of applicants for a new job is 31, with a standard deviation of 5. The hiring manager is only willing to accept applications whose age is within one standard deviation of the average age. What is the maximum number of different ages of the applicants?  Select the correct option
A) 11 B) 14 C) 15 D) 18 E) 30

Solution: within one standard deviation of the average age means 31 +/- 7   26--31--36   number of dif.ages -26 27 28 29 30 31 32 33 34 35 36   total=11   11
Answer: A
In how many different E ways can 4 ladies and 4 gentlemen be seated at a round table so that all ladies sit together?  Answers:
A) 70
B) 288
C) 576
D) 10,080
E) 20,160

Solution: Treat the 4 ladies as one object, now you have 5 objects to arrange around a table (m1,m2,m3,m4,women). This can be done in (5-1)! ways   And there are 4! ways to arrange ladies among themselves   Answer E= (4!)^2 = 576 or 576
Answer: C
0.999991+0.111119=?
Select:
A) 1
B) 1.0001
C) 1.0021
D) 1.11111
E) 1.1111

Solution: 0.999991 + 0.111119   = 0.999991 + 0.11111 + 0.00009   = (0.999991 + 0.00009) + 0.11111   = 1 + 0.11111= 
1 + 0.11111 = 1.11111
1.11111   1.11111
Answer: D
If c persons take y days to complete z similar jobs, how long does it take y persons to complete 1 such job? Select.
A) z	B) x	C) x/y	D) z/x	E) y/z

Solution: the Q doesn't seem to be having the any correct answer as a choice..   since we are looking for days, lets keep days in end and work out a solution..   c person can do z jobs in y days..   so c person can do 1 job in y/z days..   and 1 person can do 1 job in y^2/z days..   so y person can complete 1 job in y^2/zy=y/z..   so the answer should be y/z=y/z
Answer: E
Which of the following inequalities is equivalent to –2 < y< 4 ? Choose one: A) | y– 2 | < 4 B) | y– 1 | < 3 C) | y+ 1 | < 3 D) | y+ 2 | < 4 E) None of the above

Solution: First remove the mod   then set the expression to 0   then get a value of y   then add and subtract the value from the given number on the RHS   Lets try with an example (| y– 1 | < 3) --------------> | y– 1 | < 3   First remove the mod -------------------> y-1   then set the expression to 0--------------> y-1=0   then get a value of y---------------------> y=1   then add and subtract the value from the given number on the RHS   1+3= 
  1+3 = 4
4 and 1-3= -2   the range become -2 to 4 correct answer   Now try its with an incorrect option (C) | ----------> |y+ 1 | < 3   First remove the mod --------------------------> y+1   then set the expression to 0----------------------> y+1=0   then get a value of y------------------------------> y=-1   then add and subtract the value from the given number on the RHS   -1+3= 
  -1+3 = 2
2 and -1-3= -4   the range become -4 to 2 Incorrect   THE CORRECT ANSWER IS | y– 1 | < 3
Answer: B
If Suresh distributes his pens in the ratio of 1/2 : 1/4 : 1/5 : 1/7 between his four friends A, B, C and D, then find the total number of pens Suresh should have?
Choose the correct answer
A) 153  B) 150  C) 100  D) 125  E) 135

Solution: EXPLANATION:   Here, A : B : C : D = 1 / 2 : 1 / 4 : 1 / 5 : 1 / 7   1) L.C.M of 2, 4, 5, 7 is 140   2) Find the number of pens each friend received --------- (To find no. of pens each friend has, multiply the ratio with the L.C.M. calculated)   A = (1/2) x 140 = 70   B = (1/4) x 140 = 35   C = (1/5) x 140 = 28   D = (1/7) x 140 = 20   3) Total number of pens = (70 x + 35 x + 28 x + 20 x) = 153 x   Minimum number of pens (x) = 1   Therefore, total number of pens = 153 pens.   153NSWER IS 153
Answer: A
A tin of oil was 4/5 full. When 6 bottles of oil were taken out and four bottles of oil were poured into it, it was 3/4 full. how many bottles of oil can the tin contain? Choose the correct choice from the following answers:
A) 10	B) 40	C) 46	D) 36	E) 25

Solution: Suppose X bottles can fill the tin completely   Then Present oil = 4/5 X   after 6 bottles taken out it is 4/5 X - 6   after four bottles poured in it is 4/5 X - 6 + 4   now the oil level is 3/4X   so 4/5 X - 6+4 = 3/4X ===> 4/5 X - 3/4 X = 6-4   X/20=2   X=40   Therefore required no of bottles = 40   so 40 bottles of oil can fill the tin.   the answer is option 40) 40.
Answer: B
The total number of problems in the mathematics and algebra books is 28 more than the total number of problems in the algebra and geometry books. How much lesser is the number of problems in the geometry book as compared to the mathematics book?
Select the correct option:
A) 30  B) 18  C) 28  D) 25  E) 32

Solution: (Mathematics + Algebra) - (Algebra + Geometry) = 28   Mathematics - Geometry = 28   Answer: 28
Answer: C