mathewhe/aqua_rat huggingface dataset:
Question: There is a 40% chance that Germany will not win at all during the whole season. There is a 50% chance that Federer will not play at all in the whole season. What is the greatest possible probability that the Germany will win and Federer will play during the season?
(A)  50%
(B)  60%
(C)  70%
(D)  72%
(E)  80%
Rationale: There is a 40% chance that Germany will not win at all during the whole season
We can infer that there is 60% chance Germany will win .
Similarly There is a 50% chance that Federer will not play at all in the whole season
We can also infer that there is 50% chance that Federer will play.
Answer A
Answer: (A)  50%
Question: Two men started from the same place walk at the rate of 10kmph and 12kmph respectively. What time will they take to be 20 km apart, if they walk in the same direction?
(A) 5hours
(B) 10hours
(C) 8hours
(D) 10hours
(E) 12hours
Rationale: To be 2km apart they take 1 hour
To be 10km apart they take = 1/2 * 20 =10 hours
Answer is B
Answer: (B) 10hours
Question: Using all the letters of the word "NOKIA", how many words can be formed, which begin with N and end with A?
(A) 9
(B) 8
(C) 6
(D) 45
(E) 2
Rationale: There are five letters in the given word.
Consider 5 blanks ....
The first blank and last blank must be filled with N and A all the remaining three blanks can be filled with the remaining 3 letters in 3! ways.
The number of words
= 3! = 6.
Answer:C
Answer: (C) 6
Question: The area of a square is 4096 sq cm. Find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 24 cm less than the side of the square?
(A) 5:17
(B) 5:14
(C) 5:10
(D) 5:11
(E) 5:16
Rationale: Let the length and the breadth of the rectangle be l cm and b cm respectively. Let the side of the square be a cm.
a2 = 4096 = 212
a = (212)1/2 = 26 = 64
L = 2a and b = a - 24
b : l = a - 24 : 2a = 40 : 128
= 5:16
Answer:E
Answer: (E) 5:16
Question: If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is?
(A) 1/5
(B) 1/2
(C) 1/3
(D) 1/9
(E) 1/2
Rationale: 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: B
Answer: (B) 1/2
Question: The perimeters of two squares are 40cm and 32 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares.
(A) 22
(B) 24
(C) 77
(D) 99
(E) 11
Rationale: Explanation:
side of first square = 40/4 =10cm
side of second square = 32/4 = 8cm
area of third squre = 10² - 8² = 36 sq cm
side of third square = \inline {\color{Black}\sqrt{36}} = 6 cm
required perimeter = 6*4 = 24cm
Answer: B) 24
Answer: (B) 24
Question: The ages of two persons differ by 20 years. If 5 years ago, the elder one be 5 times as old as the younger one, their present ages (in years) are respectively
(A) 20,20
(B) 20,10
(C) 25,15
(D) 30,10
(E) 40,10
Rationale: Explanation:
Let their ages be x and (x + 20) years.
5 (x - 5) = (x + 20 - 5) or 4x = 40 or x = 10.
Their present ages are 30 years and 10 years
Answer: Option D
Answer: (D) 30,10
Question: The cricket team of 11members is 26yrs old & the wicket keeper is 3 yrs older. If the ages ofthese 2are excluded, the average age of theremaining players is 1 year less than the average age of the whole team. What is the average age of the team ?
(A) 19
(B) 21
(C) 23
(D) 27
(E) 30
Rationale: Let the average age of the whole team be x years.
11x - (26 + 29) = 9 (x - 1)
=> 11x - 9x = 46
=> 2x = 46
=> x = 23.
So, average age of the team is 23 years.
C
Answer: (C) 23
Question: Excluding stoppages, the speed of a bus is 50 kmph and including stoppages, it is 35 kmph.For how many minutes does the bus stop per hour?
(A) 17 minutes
(B) 18 minutes
(C) 19 minutes
(D) 16 minutes
(E) None of these
Rationale: Explanation :
In one hour
Due to stoppages, it covers 15 km less.
Time taken to cover 15 km = [15/50 * 60] min = 18 min
Answer : B
Answer: (B) 18 minutes
Question: If you flip a coin three times, what is the probability that you will get three heads?
(A) 1/4
(B) 1/5
(C) 1/6
(D) 1/7
(E) 1/8
Rationale: The probability of getting heads on a single flip is 1/2,
The probability of getting heads on each flip is P_1st * P_2nd * P_3rd,
Thus, P = (1/2)^3 = 1/8.
Answer = E
Answer: (E) 1/8
Question: Rates for having a manuscript typed at a certain typing service are $5 per page for the first time a page is typed and $3 per page each time a page is revised. If a certain manuscript has 100 pages, of which 30 were revised only once, 20 were revised twice, and the rest required no revisions, what was the total cost of having the manuscript typed?
(A) $430
(B) $620
(C) $650
(D) $680
(E) $710
Rationale: For 100-30-20=50 pages only cost is 5$ per page for the first time page is typed - 50*5=250$;
For 30 pages the cost is: first time 5$ + 3$ of the first revision - 30*(5+3)=240$;
For 20 pages the cost is: first time 5$ + 3$ of the first revision + 3$ of the second revision - 20(5+3+3)=220$;
Total: 250+240+220=710$.
Answer: E.
Answer: (E) $710
Question: All possible two factors products are formed from the numbers 1, 2, 3, 4, ....., 200. The number of factors out of total obtained which are multiples of 5 is
(A) 5040
(B) 7180
(C) 8150
(D) 7280
(E) None of these
Rationale: The total number of two factor products = 200C2. The number of numbers from 1 to 200 which are not multiples of 5 is 160. Therefore the total number of two factor products which are not multiple of 5 is 160C2. Hence,the required number of factors which are multiples of 5 = 200C2 – 160C2 = 7180.
Answer B
Answer: (B) 7180
Question: A milk man has 30 liters of milk. If he mixes 5 liters of water, which is freely available, in 20 liters of pure milk.If the cost of pure milk is Rs.18 per liter,then the profit of the milkman, when he sells all the mixture at cost price is:
(A) 20%
(B) 25%
(C) 33.33%
(D) 35%
(E) None of these
Rationale: Explanation:
when the water is freely available and all the water is sold at the price of the milk, then the water gives the profit on the cost of 30 liters of milk.
Therefore, profit percentage = 35 %. Answer: D
Answer: (D) 35%
Question: Henrikh lives x blocks from his office. It takes him 1 minute per block to walk to
work and 20 seconds per block to ride his bicycle to work. If it takes him exactly
8 minutes more to walk to work than to ride his bicycle, then x equals
(A) 4
(B) 7
(C) 12
(D) 15
(E) 20
Rationale: The best way would be...
Per km, he takes 40 secs extra if he walks
So he will take 8 mins or 8*60 secs in 8*60/40 =12 km
ANSWER:C
Answer: (C) 12
Question: Mr.Parkin invested in Fund Z and Fund B. The total amount she invested, in both funds combined, was $100,000. In one year, Fund Z paid 23% and Fund B paid 17%. The interest earned in Fund B was exactly $200 greater than the interest earned in Fund Z.How much did Ms. Morris invest in Fund Z?
(A)  $32,000
(B)  $36,000
(C)  $40,000
(D)  $42,000
(E)  $45,000
Rationale: 0.17B-0.23Z = 200 | * 100
17B-23Z=20,000
Z+B=100,000
B=100,000 - Z
17(100,000 - Z) - 23Z = 20,000
1,700,000 - 17Z - 23Z = 20,000
1,680,000 = 40Z
divide by 40
first two digits: 42...so answer is D.
Answer: (D)  $42,000
Question: 2 is what percent of 40?
(A) 0.2%
(B) 2%
(C) 5%
(D) 20%
(E) 500%
Rationale: 2= x*40/100
x = 5%
Ans; C
Answer: (C) 5%
Question: If,
1 * 3 * 5 = 16
3 * 5 * 7 = 38
Then find,
2 * 7 * 9 =?
(A) 65
(B) 68
(C) 72
(D) 80
(E) 77
Rationale: (9 * 7) + 2 = 65
A
Answer: (A) 65
Question: A woman begins bicycling with a pace of 8 kmph and she increases her pace every hour by 2 kmph. She does not increase her pace as soon as her pace reaches her maximum speed of 12 kmph. How many hours did she bicycle if she traveled 64 kms?
(A) 6 1â„7 hours
(B) 6 2â„7 hours
(C) 8 2â„7 hours
(D) 5 5â„6 hours
(E) 6 1â„3 hours
Rationale: Distance covered in first hour = 8 Ã— 1 = 8 km
Distance covered in next hour = 10 Ã— 1 = 10 km
Distance covered in next hour = 12 Ã— 1 = 12 km
Distance covered in first three hours
8 + 10 + 12 = 30 km
Remaining distance = 64 â€“ 30 = 34 km.
Now, this distance will be covered at the speed of 12 km/hr.
âˆ´ Time taken = 34â„12 = 17â„6 hour.
Total time= 3 + 1â„3 = 3 17â„6 hour = 5 5â„6 hour
Answer D
Answer: (D) 5 5â„6 hours
Question: Using all the letters of the word "NOKIASED", how many words can be formed, which begin with N and end with A?
(A) 800
(B) 720
(C) 900
(D) 300
(E) 100
Rationale: There are five letters in the given word.
Consider 8 blanks ....
The first blank and last blank must be filled with N and A all the remaining three blanks can be filled with the remaining 3 letters in 6! ways.
The number of words = 6! = 720.
Answer:B
Answer: (B) 720
Question: A man has Rs. 320 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
(A) 37
(B) 38
(C) 60
(D) 90
(E) 28
Rationale: Let number of notes of each denomination be x.
Then, x + 5x + 10x = 320 16x = 320 x = 20.
Hence, total number of notes = 3x = 60.
Answer:C
Answer: (C) 60
Question: The surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 6 cm each. The radius of the sphere is
(A) 3 cm
(B) 4 cm
(C) 6 cm
(D) 8 cm
(E) None
Rationale: Solution
4Î R2	= 2Î 3x6
â‡’ R2 = (3x6/2)
â‡’ 9
â‡’ R = 3 cm.
Answer A
Answer: (A) 3 cm
Question: A man can row upstream at 15 kmph and downstream at 25 kmph, and then find the speed of the man in still water?
(A) 27
(B) 29
(C) 30
(D) 20
(E) 24
Rationale: US = 15
DS = 25
M = (15 + 25)/2
= 20
Answer:D
Answer: (D) 20
Question: Perimeter of the back wheel = 9 feet, front wheel = 7 feet on a certain distance, the front wheel gets 10 revolutions more than the back wheel .What is the distance?
(A) 315
(B) 325
(C) 335
(D) 345
(E) 305
Rationale: for 1 revolution:front wheel goes 7 ft.and back wheel goes 9feet.
let distance is x feet.
x/7=(x/9)+10
or,2x/63=10
or,x=(10*63)/2
therefore,x=315 ANSWER:A
Answer: (A) 315
Question: x, y, and z are all unique numbers. If x is chosen randomly from the set {5, 6, 7, 8, 9, 10, 11} and y and z are chosen randomly from the set {20, 21, 22, 23}, what is the probability that x and y are prime and z is not?
(A) 1/5
(B) 3/20
(C) 1/7
(D) 2/15
(E) 3/28
Rationale: P(x is prime) = 3/7
P(y is prime) = 1/4
If y is prime, then z is not prime since y and z are unique.
Then the probability is 3/7*1/4 = 3/28
The answer is E.
Answer: (E) 3/28
Question: Let n~ be defined for all positive integers n as the remainder when (n - 1)! is divided by n.
What is the value of 31~ ?
(A) 2
(B) 1
(C) 0
(D) 8
(E) 31
Rationale: n~ = (n-1)!
so 31~ = (31-1)! = 30!
when 30!/31 we have 16*2 inside 30!
hence 31 gets cancelled and we get remainder as 0
C
Answer: (C) 0
Question: A company has 17 equally qualified applicants for 4 open positions. How many different groups of 4 applicants can be chosen by the company to fill the positions if the order of selection does not matter?
(A) 2380
(B) 2400
(C) 2420
(D) 2440
(E) 2460
Rationale: 17C4=2380
The answer is A.
Answer: (A) 2380
Question: A and B started a partnership business investing some amount in the ratio of 3 : 5. C joined then after six months with an amount equal to that of B. In what proportion should the profit at the end of one year be distributed among A, B and C?
(A) 3 : 5 : 2
(B) 3 : 5 : 5
(C) 6 : 10 : 5
(D) 5:8:10
(E) Data inadequate
Rationale: Let the initial investments of A and B be 3x and 5x.
A : B : C = (3x x 12) : (5x x 12) : (5x x 6) = 36 : 60 : 30 = 6 : 10 : 5.
Answer: (C) 6 : 10 : 5
Question: On Monday morning, Chris receives tickets to a baseball game that will be played at 7pm on the next evening that it does not rain. However, Chris is only in town until Wednesday morning, at which point he must fly to another city. If there is a 50% chance of rain each of the next two evenings, what is the probability that Chris will be able to attend the game?
(A)  36%
(B)  60%
(C)  66%
(D)  75%
(E)  84%
Rationale: Chris won't be able to attend the game if it be raining on Monday eveningandTuesday evening. The probability of that is 0.5*0.5 = 0.25. So, the probability that he will be able to attend is 1 - 0.25 = 0.75.
Answer: D.
Answer: (D)  75%
Question: A certain tire company can produce tires at a cost of $22,500 per batch plus $10 per tire. The company can sell tires to the wholesaler at a cost of $20 per tire. If a batch of 15,000
tires is produced and sold, what is the company’s profit per tire?
(A) $9.00
(B) $8.50
(C) $11.00
(D) $13.50
(E) $20.00
Rationale: CP(15000 tires) = $22500 +($10×15000) =$172500
SP (15000 tires) = $20×15000 = $300000
Profit = SP-CP
= $300000-$172500= $127500
PROFIT/TIRE = $127500/15000 = $8.50
Answer B
Answer: (B) $8.50
Question: A not-so-good clockmaker has four clocks on display in the window. Clock #1 loses 45 minutes every hour. Clock #2 gains 15 minutes every hour relative to Clock #1 (i.e., as Clock #1 moves from 12:00 to 1:00, Clock #2 moves from 12:00 to 1:15). Clock #3 loses 20 minutes every hour relative to Clock #2. Finally, Clock #4 gains 20 minutes every hour relative to Clock #3. If the clockmaker resets all four clocks to the correct time at 12 noon, what time will Clock #4 display after 6 actual hours (when it is actually 6:00 pm that same day)?
(A) 5:00
(B) 5:34
(C) 5:42
(D) 6:34
(E) 6:24
Rationale: C1 loses 15 minutes every hour. So after 60 minutes have passed, C1 displays that 60-15 = 45 minutes have passed.
C2 gains 15 minutes for every 60 minutes displayed on C1. Thus, the time displayed on C2 is 75/60 = 5/4 the time displayed on C1. So after 60 minutes have passed, C2 displays the passing of (5/4 * 45) minutes.
C3 loses 20 minutes for every 60 minutes displayed on C2. Thus, the time displayed on C3 is 40/60 = 2/3 the time displayed on C2. So after 60 minutes have passed, C3 displays the passing of (2/3 * 5/4 * 45) minutes.
C4 gains 20 minutes for every 60 minutes displayed on C3. Thus, the time displayed on C4 is 80/60 = 4/3 the time displayed on clock 3. So after 60 minutes have passed, C4 displays the passing of 4/3 * 2/3 * 5/4 * 45 = 50 minutes.
C4 loses 10 minutes every hour.
In 6 hours, C4 will lose 6*10 = 60 minutes = 1 hour.
Since the correct time after 6 hours will be 6pm, C4 will show a time of 6-1 = 6:34pm.
The correct answer is D.
Answer: (D) 6:34
Question: A man can row his boat with the stream at 22 km/h and against the stream in 10 km/h. The man's rate is?
(A) 1 kmph
(B) 2 kmph
(C) 7 kmph
(D) 6 kmph
(E) 3 kmph
Rationale: DS =22
US =10
S = ?
S = (22 - 10)/2 = 6 kmph
Answer:D
Answer: (D) 6 kmph
Question: There are 99 birds on the roof.
suddenly all birds fly away.
some birds fly to east.
birds fly to west is twice of that of east.
birds fly to north is twice of that of west.
Birds flies to south is same as in north.
Find the no. of birds fly in all diections.
(A) 99
(B) 89
(C) 79
(D) 84
(E) 74
Rationale: east= x
west= 2x
north= 4x
south=4x
x+2x+4x+4x=99
11x=99
x=9
east= 9
west= 18
north = south=36
ANSWER:A
Answer: (A) 99
Question: At a summer camp with 1,800 participants, 1/2 of the campers are aged 8 to 12. Next year, the number of campers aged 8 to 12 will increase by 1/3. After this change, what percentage of the total 1,800 campers will the 8- to 12-year-olds represent?
(A) 68%
(B) 66%
(C) 66 2/3%
(D) 60%
(E) 70%
Rationale: Total - 1,800 participants
campers are aged 8 to 12 = (1/2)*1800 = 900
Next year, campers are aged 8 to 12 = (4/3)*900 = 1200
Percentage = (1200/1800)*100 = 66 2/3%
Answer: Option C
Answer: (C) 66 2/3%
Question: John and Andy start a two-length swimming race at the same moment but from opposite ends of the pool. They swim in lanes at uniform speeds, but John is faster than Andy. They 1st pass at a point 18.5m from the deep end and having completed one length each 1 is allowed to rest on the edge for exactly 45 sec. After setting off on the return length, the swimmers pass for the 2nd time just 10.5m from the shallow end. How long is the pool?
(A) 45
(B) 50
(C) 55
(D) 60
(E) 65
Rationale: let x=length of pool
at first meeting, combined distance=x
at second meeting, combined distance=3x
if andy swims 18.5 m of x, then he will swim 3*18.5=55.5 m of 3x
andy's total distance to second meeting=x+10.5 m
x+10.5=55.5 m
x=45 m
A
Answer: (A) 45
Question: If a town of 75,000 people is growing at a rate of approx. 1% per year, the population of the town in 5 years will be closest to?
(A) a.76000
(B) b.77000
(C) c.78000
(D) d.79000
(E) e.80000
Rationale: 1% is quite small and hence the answer is A)
Answer: (A) a.76000
Question: Two pipes A and B can separately fill a tank in 2 minutes and 15 minutes respectively. Both the pipes are opened together but 4 minutes after the start the pipe A is turned off. How much time will it take to fill the tank?
(A) 9 min
(B) 10 min
(C) 11 min
(D) 12 min
(E) 13 min
Rationale: 4/12 + x/15 = 1
x = 10
ANSWER:B
Answer: (B) 10 min
Question: The product of two numbers is 120 and the sum of their squares is 289. The sum of the number is:
(A) 23
(B) 20
(C) 12
(D) 128
(E) 171
Rationale: Let the numbers be x and y.
Then, xy = 120 and x2 + y2 = 289.
(x + y)2 = x2 + y2 + 2xy = 289 + (2 x 120) = 529
x + y = 529 = 23.
ANSWER A
Answer: (A) 23
Question: If the digits 29 in the decimal 0.00029 repeat indefinitely, what is the value of (10^5-10^3)(0.00029)?
(A) 2.9e-06
(B) 2.9e-05
(C) 0.0029
(D) 29
(E) 0.29
Rationale: 99*0.29=28.71 approx. 29
Answer : D
Answer: (D) 29
Question: By selling an article at Rs.600, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 25%?
(A) s.360
(B) s.480
(C) s.500
(D) s.450
(E) s.550
Rationale: SP = 600
Profit = 25%
CP = (SP)*[100/(100+P)]
= 600 * [100/125]
= 480
Loss = 25% = 25% of 480 = Rs.120
SP = CP - Loss = 480 - 120 = Rs.360
ANSWER:A
Answer: (A) s.360
Question: The compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. The period(in years) is?
(A) 2
(B) 3
(C) 4
(D) 1
(E) 5
Rationale: Amount = (30000 + 4347) = Rs. 34347
Let the time be n years. Then,
30000(1 + 7/100)n = 34347
= (107/100)n = 34347/30000 = (107/100)2
n = 2 years.
ANSWER:A
Answer: (A) 2
Question: If a man walks to his office at ¾ of his usual rate, he reaches office 1/2 of an hour late than usual. What is his usual time to reach office?
(A) 1 1/4 hour
(B) 1 1/2 hour
(C) 1 1/3 hour
(D) 1 1/5 hour
(E) 2 1/2 hour
Rationale: Speed Ratio = 1:3/4 = 4:3
Time Ratio = 3:4
1 -------- 1/2
3 --------- ?
=> 1 1/2 hour
ANSWER:B
Answer: (B) 1 1/2 hour
Question: By selling 15 pencils for a rupee a man loses 25%. How many for a rupee should he sell in order to gain 25%?
(A) 8
(B) 7
(C) 9
(D) 4
(E) 11
Rationale: 75% --- 12
125% --- ?
75/125 * 15
= 9
Answer:C
Answer: (C) 9
Question: Out of 40 consecutive integers, two are chosen at random. Find the probability that their sum is odd?
(A) 21/40
(B) 19/39
(C) 21/39
(D) 20/39
(E) 22/39
Rationale: Forty consecutive integers will have 20 even and 20 odd integers. The sum of 2 chosen integers will be odd, only if:
First is even and second is odd
First is odd and second is even
Mathematically the probability will be given by:
P(First is even) * P(Second is odd) + P(First is odd) * P(Second is even)
= (20/40) * (20/39) + (20/40) * (20/39)
= 20/39 answer :D
Answer: (D) 20/39
Question: 2 no.'s, when divided by 17, leave remainders 13 and 11 respectively. If the sum of those 2 no.'s is divided by 17, the remainder will be
(A) 3
(B) 4
(C) 7
(D) 8
(E) 9
Rationale: (C)
Required remainder = remainder by (13 +11)/17 = 7
Answer: (C) 7
Question: A person purchased a TV set for Rs. 16000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 31150. What percentage of profit did he make?
(A) 28
(B) 27
(C) 40
(D) 99
(E) 82
Rationale: The total CP = Rs. 16000 + Rs. 6250 = Rs. 22250 and SP = Rs. 31150
Profit(%) = (31150 - 22250)/22250 * 100
= 40%
Answer:C
Answer: (C) 40
Question: A coin is tossed until sequence HTH appears (H denotes the fall of heads, T denotes the fall of tails). What is the probability Q that the game will end after the fourth throw?
(A) 1/16
(B) 3/32
(C) 1/8
(D) 3/16
(E) 1/4
Rationale: Another approach:
Two likely scenarios would be : HHTH or THTH
for each of the scenarios probability would be 1/16
So Probablilty Q is 1/16 + 1/16 = 1/8=C
Answer: (C) 1/8
Question: From the sale of sleeping bags, a retailer made a gross profit of 12% of the wholesale cost. If each sleeping bag was sold for $28, what was the wholesale cost per bag?
(A) 3.0
(B) 3.36
(C) 24.64
(D) 25.0
(E) 31.36
Rationale: Cost price * 1.12 = Selling price --> Cost price * 1.12 = $28 --> Cost price = $25.
Answer: D.
Actually even without any math only C and D make any sense, but since 24.64 * 1.12 won't be an integer ($28) then only answer choice D remains.
Answer: (D) 25.0
Question: Of the three digit integers greater than 700, how many have two digits that are equal to each other and the remaining digit different from the other two?
(A) 90
(B) 82
(C) 80
(D) 45
(E) 36
Rationale: Three digit number can have only following 3 patterns:
A. all digits are distinct;
B. two are alike and third is different;
C. all three digits are alike.
We need to calculate B. B=Total - A - C
Total numbers from 700 to 999 = 299 (3-digit numbers greater than 700);
A. all digits are distinct = 3*9*8=216 (first digit can have only three values 7, 8, or 9);
C. all three are alike = 3 (777, 888, 999).
So, 299-216-3=80.
Answer: C.
Answer: (C) 80
Question: 19/38 = 4/8 . which method did you use to determine whether this proportion is true or false?
(A) true
(B) neutral
(C) false
(D) not sure
(E) none
Rationale: 19/38= 4/8 cross multiplication: 19 *8 = 152, 4* 38 = 152,
we see that 152 are not equal to 81. so there is proportion. corrcet answer: (A)
Answer: (A) true
Question: What is the area of a square field whose diagonal of length 20 m?
(A) 300 sq m
(B) 250 sq m
(C) 200 sq m
(D) 400 sq m
(E) 450 sq m
Rationale: Explanation:
d2/2 = (20 * 20)/2 = 200
ANSWER IS C
Answer: (C) 200 sq m
Question: Mr. Johnson was to earn £ 300 and a free holiday for seven weeks' work. He worked for only 4 weeks and earned £ 30 and a free holiday. What was the value of the holiday?
(A) £ 300
(B) £ 330
(C) £ 360
(D) £ 420
(E) £ 460
Rationale: 7week=300+holiday
1 week= (300+ holiday)/7
4 week =(300+ hliday)*4/7-- eqn1
bt 4 week = 30 + holiday(given)--eqn2
equate eqn 1 and eqn 2 to get th ecost of holiday=330
ANSWER:B
Answer: (B) £ 330
Question: A bus travels k miles in n hours. How many miles will it travel in x hours at the same rate?
(A) knx
(B) k⁄n
(C) x
(D) kx⁄n
(E) kn⁄x
Rationale: Given Speed = k/n
To Find distance in x hours with same speed
Distance = speed * time
Distance = k/n*x = kx/n
Answer D
Answer: (D) kx⁄n
Question: If a, b, and c are positive integers such that a is divisible by b, and c is divisible by a, which of the following is NOT necessarily an integer?
(A) (a + c)/b
(B) (c - a)/b
(C) ca/b
(D) (c + b)/a
(E) cb/a
Rationale: a=bx.........(1)
c=aY.........(2)
a. (A+C)/B = (bx+ay)/b = (bx+ bxy)/b =x+xy=integer
b. (c-a)/b = (ay-a)/b = a(y-1)/b = bx(y-1)/b = integer.
similarly
All options were integer except D.
d.(c+b)/a
ay+b)/a .....not integer......
Ans D
Answer: (D) (c + b)/a
Question: Four years ago, P was half of Q's age. If the ratio of their present ages is 3:4 what will be the total of their present ages?
(A) 14
(B) 17
(C) 29
(D) 31
(E) 35
Rationale: Let present age of P and Q be 3x3x and 4x4x respectively.
Ten years ago, P was half of Q's age
â‡’(3xâˆ’4)=1/2(4xâˆ’4)
â‡’6xâˆ’8=4xâˆ’4
â‡’2x=4
â‡’x=2
Total of their present ages
=3x+4x=7x=7Ã—2=14
A
Answer: (A) 14
Question: If the two hands in a clock are 2 minutes divisions apart,then the angle between them is
(A) 3Â°
(B) 12Â°
(C) 24Â°
(D) 60Â°
(E) None of these
Rationale: In a clock, each minute makes 6Â°
âˆ´ 2 minutes will make 6 Ã— 2 = 12Â°
Answer B
Answer: (B) 12Â°
Question: Tom purchased 8kg of apples at the rate of 70 per kg and 9 kg of mangoes at the rate of 65 per kg. How much amount did he pay to the shopkeeper?
(A) A)1040
(B) B)1145
(C) C)1055
(D) D)1060
(E) E)1075
Rationale: Cost of 8 kg apples= 70 × 8 = 560.
Cost of 9 kg of mangoes = 65 × 9 = 585.
Total cost he has to pay = 560 + 585 = 1145.
B)
Answer: (B) B)1145