mathewhe/aqua_rat huggingface dataset:
Question: A man can do a piece of work in 5days, but with the help of his son, he can finish it in 3days. In what time can the son do it alone?
(A) 5
(B) 5 1/2
(C) 7 1/2
(D) 6
(E) 9 1/2
Rationale: Son's 1day work = 1/3 - 1/5 = 2/15
Son alone can do the work in 15/2days = 7 1/2 days
Answer is C
Answer: (C) 7 1/2
Question: The Natural Woman, a women's health food store, offers its own blends of trail mix. If the store uses 3 different ingredients, how many bins will it need to hold every possible blend, assuming that each blend must have at least two ingredients? (Also assume that each bin can hold one and only one blend.)
(A)  1
(B)  4
(C)  7
(D)  11
(E)  10
Rationale: We're told that there are 3 ingredients (we'll call them A, B, C ); we're told that each 'mix' must include AT LEAST 2 ingredients...
2 ingredient blends:
AB
AC
BC
3 ingredient blends:
ABC
Total blends = 3+1= 4
B
Answer: (B)  4
Question: The largest natural number which exactly divides the product of any four consecutive natural numbers is:
(A) 6
(B) 12
(C) 24
(D) 120
(E) 160
Rationale: Required number= 1*2*3*4=24
Answer: C
Answer: (C) 24
Question: If 7 is 10 percent of 50 percent of a certain number, what is the number?
(A) 150
(B) 217
(C) 100
(D) 90
(E) 140
Rationale: Using elimination method to pick the correct option it will be discovered that option E i.e 140 is the correct option because 50% of 140 is 70 and 10% of 70 is 7.
ANSWER:E
Answer: (E) 140
Question: A man spends Rs. 1500 per month on an average for the first three months, Rs 1550 for next four months and Rs. 1800 per month for the last five months and saves Rs . 5200 a year. What is his average monthly income?
(A) 2075
(B) 2100
(C) 2200
(D) 2300
(E) 2400
Rationale: Explanation:
Total expenditure for the first 3 months = 3 Ã— 1500 = 4500
Total expenditure for 4 months = 4 Ã— 1550 = 6200
Total expenditure for 5 months = 5 Ã— 1800 = 9000
Total expenditure and saving (which is income for one year)
= 4500 + 6200 + 9000 + 5200 = Rs. 24900
So, Average monthly income = 24900/12 = Rs. 2075
Answer A
Answer: (A) 2075
Question: A thief runs away from A with a speed of 20 km/hr. A police from a station 60 km away started chasing him after 1 hr. with a speed of 40 km/hr. Time taken by the police to catch the thief is :
(A) 4 hrs
(B) 4.5 hrs
(C) 5.4 hrs
(D) 6 hrs.
(E) None of these
Rationale: Explanation :
Solution: Distance traveled by the thief in 1 hr. = 20 km.
Total distance of them after 1 hr = (60 + 20) km = 80 km.
Their relative speed = (40 - 20) = 20 km/hr.
Time taken to catch the thief = 80/20 = 4 hrs.
Answer : A
Answer: (A) 4 hrs
Question: A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12100 after a year?
(A) 3630
(B) 3631
(C) 3639
(D) 3637
(E) 3633
Rationale: 6300:4200:10500
3:2:5
3/10 * 12100 = 3630
Answer:A
Answer: (A) 3630
Question: 15 times a number gives 150. The number is
(A) 11
(B) 15
(C) 13
(D) 14
(E) Cannot be determined
Rationale: Explanation:
Let the number be 'N'
15×N=150⇒N=10
Correct Option: B
Answer: (B) 15
Question: There are five thieves, each loot a bakery one after the other such that the first one takes 1/2 of the total no. of the breads plus 1/2 of a bread. Similarly 2nd, 3rd,4th and 5fth also did the same. After the fifth one no. of breads remained are 3. Initially how many breads were there?
(A) 124
(B) 125
(C) 126
(D) 127
(E) 128
Rationale: Let the Number of Breads Initial be x
You Should Go in Reverse Order as left Bread is 3
i.e x=?
After 1st person ate A=x-(x/2)-(1/2)
i.e A=(2x-x)/2-(1/2)
i.e A=(x/2)-(1/2)
i.e A=(2x-2)/4
i.e A=(x-1)/2
like wise ----After 2nd person ate B=(A-1)/2
like wise ----After 3rd person ate C=(B-1)/2
like wise ----After 4th person ate D=(C-1)/2
like wise ----After 5th person ate E=(D-1)/2
Now as after 5th person ate the Value of remaining Bread is ---3
therefore the value of E=3;
Now go Reverse from botom to top to get the value of X after calcuating
Value of D=7
Value of C=15
Value of B=31
Value of A=63
Value of X=127
SO the Final answer is 127 breads were there
ANSWER:D
Answer: (D) 127
Question: 3 candidates in an election and received 1136, 7636 and 11628 votes respectively. What % of the total votes did the winningcandidate got in that election?
(A) 45%
(B) 47%
(C) 57%
(D) 48%
(E) 50%
Rationale: Total number of votes polled = (1136 + 7636 + 11628) = 20400
So, Required percentage = 11628/20400 * 100 = 57%
C
Answer: (C) 57%
Question: In a joint business, the capital of A, B and C were Rs. 45000, Rs. 30000 and Rs. 22500 respectively. A withdrew half of his capital after 4 months. After 9 months of this withdrawal, there was a total profit of Rs. 28400. Find the A share of profit?
(A) 10600
(B) 10400
(C) 10200
(D) 12200
(E) 14200
Rationale: Given A=45000 B=30000 C=22500
A:B:C= 450:300:225
As A withdrew its half of capital after 4 months,it can withdraw 22500 rupees
But before 4 months, it is 45000 only and the profit is calculated after withdrwal it is almost 9+4=13 months.For that 9 months, the capital for A is half of its original capital,
So A= 450*4+ 225*9= 1800+2025= 3825
Similarly, B= 300*13=3900
Similarly,C= 225*13= 2925
Therefore, ratio of A:B:C= 3825: 3900 : 2925= 51:52:39
A's share=51/142(28400)=10200
ANSWER:C
Answer: (C) 10200
Question: A train 125 m long passes a man, running at 11 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?
(A) 37 km/hr
(B) 50 km/hr
(C) 56 km/hr
(D) 26 km/hr
(E) 87 km/hr
Rationale: Speed of the train relative to man = 125/10 = 25/2 m/sec.
= 25/2 * 18/5 = 45 km/hr
Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.
x - 11 = 45 => x = 56 km/hr.
Answer:C
Answer: (C) 56 km/hr
Question: A sum of money at simple interest amounts to Rs. 825 in 3 years and to Rs. 854 in 4 years. The sum is?
(A) Rs. 738
(B) Rs. 638
(C) Rs. 650
(D) Rs. 730
(E) Rs. 735
Rationale: S.I. for 1 year = (854 - 825) = Rs. 29
S.I. for 3 years = 29 * 3 = Rs. 87
Principal = (825 - 87) = Rs. 738.
ANSWER:A
Answer: (A) Rs. 738
Question: Sachin is younger than Rahul by 6 years. If their ages are in the respective ratio of 7 : 9, how old is Sachin?
(A) 16
(B) 18
(C) 28
(D) 30
(E) 34
Rationale: Let Rahul's age be x years.
Then, Sachin's age = (x - 6) years.
(x - 6)/x	=	7/9
9x - 54 = 7x
2x = 54
x = 27
Hence, Sachin's age =(x - 7) = 34 years.
Ans-E
Answer: (E) 34
Question: A vessel was filled with 10 ounces of liquid, and 0.008 ounce of the liquid evaporated each day during a 50-day period. What % of the original amount of liquid evaporated during this period?
(A) 0.004%
(B) 4%
(C) 5%
(D) 60%
(E) 40%
Rationale: Total amount of water evaporated each day during a 50-day period = .008 * 50
=.008 * 100/2
= .8/2
= .4
percent of the original amount of water evaporated during this period = (.4/10) * 100%
= 4 %
Answer B
Answer: (B) 4%
Question: At 1:00 pm, a truck left city P and headed toward City Q at a constant speed of 36 km/h. One hour later, a car left City Q and headed toward City P along the same road at a constant speed of 48 km/h. If the distance between City P and City Q is 330 km, at what time will the truck and the car meet each other?
(A) 4:30
(B) 4:45
(C) 5:00
(D) 5:15
(E) 5:30
Rationale: At 2:00 pm, the truck and the car are 294 km apart.
The truck and the car complete a distance of 84 km each hour.
The time it takes to meet is 294/84 = 3.5 hours.
They will meet at 5:30 pm.
The answer is E.
Answer: (E) 5:30
Question: If SAVOURY is coded as OVUARSY then how will RADIATE be coded?
(A) AIDARET
(B) IDARATE
(C) ARIADTE
(D) IDAATRE
(E) None of these
Rationale: Comparing the positions of letters S,A,V,O,U,R,Y in SAVOURY and OVUARSY :-
letters at 1,2,3,4,5,6,7 position in SAVOURY have their sequence changed as 4352617 in OVUARSY(4th letter O comes at 1st position, 3rd at 2nd,..)
Similarly, juxtapositioning the letters of RADIATE, i.e. keeping 4th letter(I) at 1st position, 3rd (D) at 2nd position,... and so on..we get
IDAATRE
ANSWER:D
Answer: (D) IDAATRE
Question: Mrudul invested an amount of Rs.29500/- in order to start a business. Shalaka joined her 4 months later by investing an amount of Rs.33500/-. If the business earned a profit of Rs.120575/- at the end of two years, what was Mrudul’s share of the profit?
(A) Rs.60725/-
(B) Rs.61950/-
(C) Rs.59250/-
(D) Rs.58625/-
(E) None of these
Rationale: Explanation:
Ratio of Mrudul’s profit and Shalaka’s profit = 29500x24/33500x20 = 354 : 335
:. Mrudul’s share out of total profit = 120575x354/689 = Rs.61950
Answer: Option B
Answer: (B) Rs.61950/-
Question: A can do a piece of work in 8 days and B alone can do it in 12 days. How much time will both take to finish the work ?
(A) A)4.8
(B) B)6.333
(C) C)7.333
(D) D)8.5
(E) E)9
Rationale: This question can be solved by different methods. We need to conserve time in exams so solving this problem using equations is the good idea.
Time taken to finish the job = XY / (X + Y)
= 8 x 12 / (8 + 12)
= 96 / 20
= 4.8 days
Answer: A
Answer: (A) A)4.8
Question: A no. when divided successively by 4 and 5 leaves remainders 1&4 respectively. What willbe the respective remainders if it is successively divided by 5 and 4?
(A) 1, 2
(B) 2, 3
(C) 2, 5
(D) 2, 7
(E) 3, 5
Rationale: Let
p
p be the number
Suppose,
p
÷
4
=
q
p÷4=q, remainder = 1
q
÷
5
=
1
q÷5=1, remainder = 4. (Note that we assumed the quotient as 1 for the ease of calculations.)
Hence,
q
=
1
×
5
+
4
=
9
q=1×5+4=9
p
=
4
q
+
1
=
4
×
9
+
1
=
37
p=4q+1=4×9+1=37
Now divide 37 successively by 5 and 4 respectively.
37÷5=7
37÷5=7, remainder = 2
7÷4=1
7÷4=1, remainder = 3
B
Answer: (B) 2, 3
Question: Murthy secured 70% of the votes in an election and was elected by a majority of 168 votes. All of the votes polled were valid. Find out number of votes polled if there were only two contestants ?
(A) 410
(B) 420
(C) 430
(D) 440
(E) 450
Rationale: Let the No. of votes polled is x
Then, Murthy got=(7/10)x
and the loser got=(3/10)x
As per the condition
(7/10)x-(3/10)x=168
Solving, we get x = 420
Thus, the no. of votes polled =420
ANSWER:B
Answer: (B) 420
Question: The distance between 2 cities A and B is 330km. A train starts from A at 8 a.m. and travels towards B at 60 km/hr. Another starts from B at 9 a.m. and travels towards A at 75 km/hr. At what time do they meet?
(A) 9a.m.
(B) 10a.m.
(C) 10.30a.m.
(D) 11a.m.
(E) 1p.m.
Rationale: Suppose they meet x hrs after 8 a.m.
Distance moved by first in x hrs + Distance moved by second in (x-1)hrs = 330
60x + 75 (x-1) = 330
x = 3
They meet at 8+3 = 11 a.m.
Answer is D
Answer: (D) 11a.m.
Question: Two identical circles intersect such that their centers and the points at which they intersect form a square of side 0.5 cm. What is the area of the region where the two circles intersect?
(A) 2pi - 4
(B) pi -2
(C) pi/2 - 1
(D) pi/4 - 0.5
(E) pi/8 - 0.25
Rationale: Drawing a diagram, we see that the radius of the circle equals the side of the square.
The area of intersection is: pi*r^2/4 - (r^2-pi*r^2/4) = pi*r^2/2 - r^2 = pi/8 - 0.25
The answer is E.
Answer: (E) pi/8 - 0.25
Question: Three partners A,B,C starts a business. Twice A's capital is equal to thrice B's capital and B's capital is four times C's capital. Out of a total profit of Rs.17000 at the end of the year, B's share is
(A) Rs.4000
(B) Rs.6120
(C) Rs.7500
(D) Rs.6600
(E) None
Rationale: Solution
Let C = x.
Then, B = 4x and 2A = 3x4x = 12x or A = 6x.
âˆ´ A : B : C = 6x : 4x : x	= 6 : 4 : 1.
So B's capital	= Rs(17000 x 4 / 11)
= Rs.6120.
Answer B
Answer: (B) Rs.6120
Question: A and B can do a piece of work in 12 days and 16 days respectively. Both work for 3 days and then A goes away. Find how long will B take to complete the remaining work?
(A) 6 days
(B) 9 days
(C) 18 days
(D) 24 days
(E) 4 days
Rationale: Explanation:
3/12 + (3 + x)/16 = 1
x = 9 days
Answer B
Answer: (B) 9 days
Question: A car covers a distance of 424 km in 6 ½ hours. Find its speed?
(A) 65.9 kmph
(B) 75.2 kmph
(C) 65.2 kmph
(D) 66.2 kmph
(E) 55.2 kmph
Rationale: 424/(13/2) = 424*2/13
=65.2 kmph
ANSWER:C
Answer: (C) 65.2 kmph
Question: The distance between two towns is 380 km. At the same moment, a passenger car and a truck start moving towards each other from different towns. They meet 4 hours later. If the car drives 5 km/hr faster than the truck, what is the speed of the car?
(A) 30km/h
(B) 40km/h
(C) 50km/h
(D) 60km/h
(E) 80km/h
Rationale: The main idea used in this kind of problems is that the distance equals speed multiplied by time S=V⋅t
Car	x + 5 (V (km/hr)) 4 t (hr) 4(x +5) S (km)
Truck X V (km/hr) 4 t (hr) 4x S (km)
4(x+5)+4x=380
4x+4x=380−20
8x=360
x=3608
x=45
Therefore the truck's speed is 45 km/hr, and the car's speed is 45+5=50 km/hr
correct answer is C)50km/hr
Answer: (C) 50km/h
Question: If m = 3^n, what is the greatest value of n for which m is a factor of 22!
(A) 8
(B) 10
(C) 9
(D) 14
(E) 16
Rationale: Solution-
Consider multiples of 25!=> 3,6,9,12,15,18,21
Count no. of 3 in each multiple.
3=3x1->1
6=3x2->1
9=3x3->2
12=3x4->1
15=3x5->1
18=3x3x2->2
21=3x7->1
---- count 3's =9 so answer is 9
Answer : C
Answer: (C) 9
Question: Each writer for the local newspaper is paid as follows: a dollars for each of the first y stories each month, and a + b dollars for each story thereafter, where a > b. How many more dollars will a writer who submits y+ a stories in a month earn than a writer who submits y+ b stories?
(A) (a – b)( a + b + y)
(B) a – b
(C) a^2 – b^2
(D) y( a – b)
(E) ay + by – ay
Rationale: total earned for y+a stories =a + a(a+b)
total earned for y+b stories =a+ b(a+b)
difference = a+a(a+b) -a -b(a+b)
=(a+b)(a-b) =a^2-b^2
answer is C
Answer: (C) a^2 – b^2
Question: If it would take one machine 20 minutes to fill a large production order and another machine 30 minutes to fill the same order, how many minutes would it take both machines working together, at their respective rates, to fill the order?
(A) 10min
(B) 12min
(C) 15min
(D) 20min
(E) 18min
Rationale: This question can be solved using the Work Formula:
Work = (A)(B)/(A+B) where A and B are the individual completion rates of the respective entities (for the same job).
We're told that one machine takes 10 minutes to complete a job and another machine takes 12 minutes to complete the same job. Plugging in those values gets us...
(20)(30)/(20+30) = 600/50 = 12 minutes
Answer is B
Answer: (B) 12min
Question: There are five boxes in cargo hold. The weight of the first box is 200 kg and the weight of the second box is 20% higher than the weight of the third box, whose weight is 25% higher than the first box's weight. The fourth box at 350 kg is 30% lighter than the fifth box. Find the difference in the average weight of the four heaviest boxes and the four lightest boxes.
(A) 51.5 kg
(B) 75 kg
(C) 37.5 kg
(D) 112.5 kg
(E) None of these
Rationale: Solution: The weight of boxes is;
1st box = 200 kg;
3rd box = 250 kg;
2nd box = 300kg;
4th box = 350 kg;
5th box = 500 kg.
Hence, difference between heavier 4 and lighter 4 is 300.
Hence, difference in average is 75.
Answer: Option B
Answer: (B) 75 kg
Question: Simple interest on a sum at 4% per annum for 2 years is Rs.80. The C.I. on the same sum for the same period is?
(A) 81.6
(B) 81.9
(C) 81.3
(D) 81.1
(E) 81.4
Rationale: SI = 40 + 40
CI = 40 + 40 + 1.6 = 81.6
Answer:A
Answer: (A) 81.6
Question: Jack have 5200 meats.If exactly 30% of the meats are roast. What Percentage(approximately) of Unroast Meats so that half of the meats are roast?
(A) 27
(B) 26.5
(C) 27.32
(D) 29
(E) 28
Rationale: Number of meats=5200
Currently roast=5200*30/100=1560
Unroast meats=5200-1560=3640
Half of all Meats=2600
The number of meats to be roast to make half of all meats roast =2600-1560=1040
So now the question remains - 1040 is how much percentage of unroast meats (3640)
= 1040*100/3640
=28.57~28
Answer (E)
Answer: (E) 28
Question: Ram spends 30% of his salary on house rent, 30% of the rest he spends on his children's education and 24% of the total salary he spends on clothes. After his expenditure, he is left with Rs. 2500. What is Ram's salary?
(A) Rs. 11,494.25
(B) Rs. 20,000
(C) Rs. 10,000
(D) Rs. 15,000
(E) None of these
Rationale: Solution: Let Ram's salary be x.
He spends on rent = 30% of x = 30x/100.
He spends on education = 30% from rest of the salary= (30*70x)/(100*100) = 21x/100.
He Spends on clothes = 24% of total salary = 24x/100.
Saving = 2500.
Salary of ram = x.
(30x/100) + (21x/100) + (24x/100) + 2500 = x.
(75x/100) = x-2500.
75x = 100x-250000.
Or, 100x-77x = 250000.
Or, x = 250000/25.
Or, x = 10000.
Ram's salary = Rs. 10000.
Answer: Option C
Answer: (C) Rs. 10,000
Question: If s and t are positive integers such that s/t = 64.12, which of the following could be the remainder when s is divided by t ?
(A) 2
(B) 4
(C) 8
(D) 20
(E) 45
Rationale: s/t = 64.12
= 64+12/100
= 64+3/25
i got 3, and in the options the multiple of is 45
Answer - E
Answer: (E) 45
Question: Look at this series: 58, 52, 46, 40, 34, ... What number should come next?
(A) 26
(B) 28
(C) 30
(D) 32
(E) 34
Rationale: Explanation: This is a simple subtraction series. Each number is 6 less than the previous number.
Answer: Option B
Answer: (B) 28
Question: The symphony sells two kinds of tickets: orchestra, for $30, and upper tiers, for $12. On a certain night, the symphony sells 90 tickets and gets $1980 in revenue from the sales. How many orchestra tickets did they sell?
(A) 20
(B) 30
(C) 40
(D) 50
(E) 60
Rationale: Let x be the number of orchestra tickets.
Then 90-x is the number of upper tier tickets.
30x + 12(90-x) = 1980
18x = 1980-1080
x = 50
The answer is D.
Answer: (D) 50
Question: If, 6 years ago, Jamie was half as old as he is now, how old will he be in x years?
(A) x + 12
(B) x + 5
(C) x + 2
(D) x – 5
(E) 2x
Rationale: let his age be a. a-6=a/2 hence a=12. 12 years hence, a =x+12
Answer A
Answer: (A) x + 12
Question: Evaluate: 20 - 16÷4×3 =
(A) 16
(B) 10
(C) 4
(D) 8
(E) 6
Rationale: According to order of operations, 16÷4×3 (division and multiplication) is done first from left to right
16÷4×3 = 4 × 3 = 12
Hence
20 - 16÷4×3 = 20 - 12 = 8
correct answer D) 8
Answer: (D) 8
Question: The incomes of A and B are in the ratio 3:2 and their expenditure are in ratio 5:3. If each saves Rs. 1000, then, A's income can be:
(A) Rs. 3000
(B) Rs. 4000
(C) Rs. 6000
(D) Rs. 9000
(E) Rs. 4500
Rationale: Solution: Let income of A and B be 3x and 2x respectively. Also, their expenditure is 5y and 3y.
Now, according to question,
3x-5y = 1000 ------- (i)*3
2x-3y = 1000	---------- (ii)*5
9x-15y-10x+15y = 3000-5000;
Or, -x = -2000;
Or, x = 2000;
Then, income of A = 3x = 3*2000 = Rs. 6000.
Answer: Option C
Answer: (C) Rs. 6000
Question: If A, B and C together can finish a piece of work in 4 days. A alone in 6 days and B in 18 days, then C alone can do it in?
(A) 1
(B) 7
(C) 8
(D) 9
(E) 36
Rationale: C = 1/4 - 1/6 – 1/18 = 1/36 => 36 days'
Answer: E
Answer: (E) 36
Question: In her backyard, Florry grows only yellow roses and white roses. Some of the rose bushes have flowers of both colors, and some have flowers of one color only. The number of rose bushes that have only yellow roses is 50% greater than the number of rose bushes that have only white roses. If there are yellow roses on 80% of Florry's rose bushes, then what percent W of her bushes have only yellow roses?
(A) 20
(B) 30
(C) 50
(D) 70
(E) 80
Rationale: let, the number of bushes with only yellow flowers be x
so, number of bushes with only yellow flowers will be 1.5x
if total number of bushes of flowers= T
then total number of bushes with yellow flowers= 0.8T
we can say that total number of bushes with yellow flowers+ bushes with only white flowers= total number of bushes with flowers
so, W=0.8T+x=T
x=0.2T
so, 1.5x=0.3T
30% flowers are yellow flowers
OA B
Answer: (B) 30
Question: A shopkeeper fixes the marked price of an item 25% above its cost price. The percentage of discount allowed to gain 8% is
(A) 11.59%
(B) 12.59%
(C) 13.59%
(D) 14.59%
(E) None of these
Rationale: Explanation:
Let the cost price = Rs 100
then, Marked price = Rs 125
Required gain = 8%,
So Selling price = Rs 108
Discount = 125 - 108 = 17
Discount% = (17/135)*100 = 12.59%
Option B
Answer: (B) 12.59%
Question: Two taps can separately fill a cistern 10 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 18 minutes. The waste pipe can empty the full cistern in?
(A) 23
(B) 5
(C) 9
(D) 28
(E) 6
Rationale: 1/10 + 1/15 - 1/x = 1/18
x = 9
ANSWER C
Answer: (C) 9
Question: 2 persons can finish a job in 8 days. First person alone can finish the work in 24 days. How many days does the second person take to finish the job?
(A) 10 days
(B) 12 days
(C) 14 days
(D) 16 days
(E) 18 days
Rationale: 2 persons can do work in 1 day = 1/8
First person can do work in 1 day = 1/24
Second person can do work in 1 day = 1/8-1/24 = 1/12
So Second person can finish work in 12 days
ANSWER:B
Answer: (B) 12 days
Question: Mother, daughter and an infant combined age is 74, and mother's age is 46 more than daughter and infant. If infant age is 0.4 times of daughter age, then find daughters age.
(A) 22
(B) 10
(C) 37
(D) 38
(E) 32
Rationale: Assume M + D + I = 74; .................(1)
Also given M - D - I = 46 ⇒⇒ M = D + I + 46
Also I = 0.4 D ⇒⇒ I = 2/5 D
Substituting M and I values in the first equation we get D - 2525D - 46 + D + 2525D = 74
Solving D = 10
Answer:B
Answer: (B) 10
Question: On day one, a store sold 125 bags. On each of the next d days, the company sold 83 bags. If the average daily sales of bags over this time period (including day one) is 90 bags, what is the value of d?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: 125 + 83d = 90(d+1).
7d = 35.
d = 5.
The answer is B.
Answer: (B) 5
Question: Walking at 8KMPH From Point T to Point railway station, mike will miss the train by 5 minutes. If he walks at 10KMPH he will reach the station by 5 minutes early.What is the distance between Point T to Railway station?
(A) A)9KM
(B) B)6.66KM
(C) C)7.25KM
(D) D)12.40KM
(E) E)13KM
Rationale: Since time differences given are in minutes so let's convert speed in Km per minute
8 kmph = 8/60 km per minute = (2/15) km per minute
10 kmph = 10/60 km per minute = (1/6) km per minute
Let, Time of train to depart from station = t minutes
Distance between Point T and Railway Station = Speed*Time = (2/15)*(t+5)
Distance between Point T and Railway Station = Speed*Time = (1/6)*(t-5)
i.e. (2/15)*(t+5) = (1/6)*(t-5)
i.e. 12t+60 = 15t - 75
i.e. 3t = 135
i.e. t = 45 minutes
i.e. Distance = (1/6)*(t-5) = (1/6)*(45-5) = 40/6 = 20/3 Km = 6.66 Km
Answer: Option B
Answer: (B) B)6.66KM
Question: A number is doubled and 7 is added. If resultant is trebled, it becomes 99. What is that number
(A) 8
(B) 10
(C) 14
(D) 13
(E) 16
Rationale: Explanation:
=> 3(2x+7) = 99
=> 2x+7 = 33
=> x = 13
Option D
Answer: (D) 13
Question: A book club rented the party room of a local restaurant to meet and discuss its current novel over dinner. The total charge, including food and service, was $ 780. If each member of the club paid at least $ 42, then what is the greatest possible number of members in the club?
(A) 19
(B) 20
(C) 21
(D) 23
(E) 25
Rationale: Given: Each person spends $42.
By looking at the options, we see that if there were 20 members, each person will spend atleast $42.
Hence the greatest number of members = 19. Option A
Answer: (A) 19
Question: x is a positive integer less than 300. When x is divided by 7, the remainder is 1; when x is divided by 3, the remainder is 2. How many x are there?
(A) 21
(B) 22
(C) 23
(D) 24
(E) 25
Rationale: the nubmer which when divided by 7 leaves remainder 1 should be of the form 7k+1
this number when divided by 3 leaves remainder 2.
so,
(7k+1)-2 should be divisible by 3 or 7k-1 should be divisible by 3.
we now put the values of k starting from 0 to find first number divisible by 3
we find 1st number at k= 1
thus smallest number will be 7(1)+1 = 8
now,
next number will be = 8+ lcm of 37
i.e 29
now we will find number of all such values less than 500 by using the formula for last term of an a.p
8+(n-1)21=300
n=22.13
or n= 22
Answer:- B
Answer: (B) 22