mathewhe/aqua_rat huggingface dataset:
Question: If a, t, and c are consecutive even integers and a < t < c, all of the following must be divisible by 4 EXCEPT
(A) a + c
(B) t + c
(C) ac
(D) (bc)/2
(E) (abc)/4
Rationale: 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 - atc/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 - b + 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.B
Answer: (B) t + c
Question: The difference between a two digit number and the number obtained by interchanging the positions of its digit is 36. What is the difference between the two digits of that number?
(A) 3
(B) 4
(C) 9
(D) 8
(E) 7
Rationale: Let the ten’s digit be x
Unit’s digit be y
Then (10x+y)-(10y+x)=36
9(x-y)=36
x-y=4
Option B
Answer: (B) 4
Question: How many positive numbers not greater than 4300 can be formed using the digits 0,1,2,3,4 where repeatation is allowed?
(A) 576 numbers
(B) 575
(C) 620
(D) 640
(E) 660
Rationale: 1 digit = 5
2 digits = 4* 5 = 20
3 digits = 4*5*5= 100
Now,4 digit number till 4000 can have digits 1,2,3 in thousands place ( total choices = 3 )
0,1,2,3,4 in hundreds ,tens and ones place
I.e 3*5*5*5 = 375
Now From 4000 to 4299 = 1*3*5*5 =75
Total = 5+20+100+375+75+1 =576 (1 for 4300)
ANSWER:A
Answer: (A) 576 numbers
Question: A train crosses a platform of 200 m in 20 sec, same train crosses another platform of length 350 m in 25 sec. then find the length of the train?
(A) 150m
(B) 180m
(C) 400m
(D) 250m
(E) 155m
Rationale: Length of the train be ‘X’
X + 200/20 = X + 350/25
5X + 1000 = 4X + 1400
X = 400m
Answer:C
Answer: (C) 400m
Question: The ratio of three numbers is 5:3:4 and their sum is 108. The second number of the three numbers is?
(A) 13
(B) 16
(C) 27
(D) 29
(E) 30
Rationale: 5:3:4
Total parts = 12
12 parts --> 108
1 part ---->9
The second number of the three numbers is = 3
3 parts ----> 27
C)
Answer: (C) 27
Question: A and B starts a business with Rs.8000 each, and after 4 months, B withdraws half of his capital . How should they share the profits at the end of the 16 months?
(A) 18:11
(B) 16:11
(C) 18:19
(D) 18:121
(E) 18:112
Rationale: A invests Rs.8000 for 16 months, but B invests Rs.8000 for the first 4 months and then withdraws Rs.4000. So, the investment of B for remaining 14 months is Rs.4000 only.
A : B
8000*16 : (8000*4) + (4000*14)
128000 : 88000
A:B = 16:11.Answer:B
Answer: (B) 16:11
Question: Worker A takes 10 hours to do a job. Worker B takes 12 hours to do the same job. How long it take both A & B, working together but independently, to do the same job?
(A) 40 days
(B) 40/9 days
(C) 60/11 days
(D) 30/9 days
(E) 60/9 days
Rationale: A's one hour work = 1/10.
B's one hour work = 1/12.
(A+B)'s one hour work = 1/10+1/12 = 11/60.
Both A & B can finish the work in 60/11 days
C
Answer: (C) 60/11 days
Question: The simple form of the ratio 4/2:2/5 is?
(A) 10:6
(B) 5:1
(C) 15:3
(D) 25:3
(E) 30:3
Rationale: 4/2 : 2/5 = 20:4 = 5:1
ANSWER:B
Answer: (B) 5:1
Question: What is the smallest no. which must be added to 8261955 so as to obtain a sum which is divisible by 11?
(A) 1
(B) 2
(C) 4
(D) 6
(E) 8
Rationale: For divisibility by 11, the difference of sums of digits at even and odd places must be either zero or divisible by 11.
For 8261955, Difference =(8+6+9+5) -(2+1+5)=28-8=20.
The units digit is at odd place. So we add 2 to the number
=> 8261955 +2 = 8261957
Now , (8+6+9+7) -(2+1+5)=30-8=22 => 22 is a multiple of 11 and hence 8261957 is also divisible by 11
B
Answer: (B) 2
Question: A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 700 m long?
(A) 94sec
(B) 90sec
(C) 85sec
(D) 80sec
(E) 76sec
Rationale: Speed = 240/24 = 10 m/sec.
Required time = (240 + 700)/10 = 94 sec.
Answer:A
Answer: (A) 94sec
Question: There are 5 cars to be displayed in 5 parking spaces with all the cars facing the same direction. Of the 5 cars, 3 are red, 1 is blue and 1 is yellow. If the cars are identical except for color, how many different display arrangements of the 5 cars are possible?
(A) 20
(B) 25
(C) 40
(D) 60
(E) 125
Rationale: I think the above logic is correct except one thing:
# of arrangements is 5!3!=205!3!=20.
But a car can be arranged facing TWO directions (within one particular parking space), so we should multiply 20 by 2, 20∗2=4020∗2=40
Answer: C.
Answer: (C) 40
Question: If w is 40 percent less than e, e 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?
(A) 4%
(B) 18%
(C) 36%
(D) 40%
(E) 50%
Rationale: GIven w= 0.6e, e=0.6y, z=0.54y, substituting, w=2/3 Z----> z= 1.5w and thus z is 50% greater than w. E is the correct answer.
Answer: (E) 50%
Question: Which of the following is NOT the sum of the squares of two integers?
(A) 36
(B) 37
(C) 65
(D) 146
(E) 147
Rationale: List the numbers that are smaller than the given options - 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144.
(A) 36 - 9+25. NO.
(B) 37 - 1+36. NO.
(C) 65 - 1+64. NO.
(D) 146 - 25+121. NO.
(E) - must be the answer.
ANSWER:E
Answer: (E) 147
Question: Which of the following cannot be the square of an integer
(A) 275625
(B) 385641
(C) 227529
(D) 261121
(E) 426408
Rationale: The square of an integer (n^2) can have only the following units digit:
0, if the units digit of n is 0;
1, if the units digit of n is 1 or 9;
4, if the units digit of n is 2 or 8.
5, if the units digit of n is 5;
6, if the units digit of n is 6 or 4;
9, if the units digit of n is 3 or 7.
As, you can see the square of an integer cannot have the units digit of 2, 3, 7, or 8.
Answer: E.
Answer: (E) 426408
Question: Two cubes of their volumes in the ratio 64 : 125. The ratio of their surface area is:
(A) 1.5:5
(B) 2:5
(C) 3:5
(D) 1:5
(E) 4:5
Rationale: The ratio of their surface area is
64 : 125
4 : 5
Answer is E.
Answer: (E) 4:5
Question: Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is ?
(A) 17/26
(B) 17/29
(C) 17/24
(D) 17/20
(E) 17/21
Rationale: n(S) = 20
n(Even no) = 10 = n(E)
n(Prime no) = 8 = n(P)
P(EᴜP) = 10/20 + 8/20 - 1/20 = 17/20
Answer: D
Answer: (D) 17/20
Question: What is the banker's discount if the true discount on a bill of Rs.540 is Rs.90 ?
(A) Rs. 108
(B) Rs. 120
(C) Rs. 102
(D) Rs. 106
(E) None of these
Rationale: Explanation :
Present Worth, PW = F - TD = 540 - 90 = Rs. 450
Simple Interest on the Present Worth = True Discount
Hence Simple Interest on 450 = 90 ------(Equation 1)
Simple Interest on the face value = Bankers Discount
=> Simple Interest on 540 = Bankers Discount
From Equation 1, Simple Interest on 450 = 90
Hence, Simple Interest on 540 = 90/450×540=540/5 = Rs. 108
=> Bankers Discount = Rs. 108 Answer : Option A
Answer: (A) Rs. 108
Question: In one year, the population, of a village increased by 10% and in the next year, it decreased by 10%. If at the end of 2nd year, the population was 7920, what was it in the beginning?
(A) 3337
(B) 8000
(C) 2788
(D) 2999
(E) 1121
Rationale: x*110/100 * 90/100 = 7920
X*0.99=7920
X=7920/0.99
=> 8000
Answer: B
Answer: (B) 8000
Question: During a trip, Francine traveled x percent of the total distance at an average speed of 40 miles per hour and the rest of the distance at an average speed of 80 miles per hour. In terms of x, what was Francine's average speed for the entire trip?
(A) (180-x)/2
(B) 4800/x+60
(C) (300-x)/5
(D) 600/(115-x)
(E) 12,000/(x+200)
Rationale: total distance =100 ;total time = T
t1 = x/40 t2 = 100-x /80
T =t1+t2 = x/30 + 100-x/80 = (80x + 3000- 30x)/2400
= (50x+3000)/2400
= x +60 / 48
av speed = 100*48/x+60 = 4800/x+60
B
Answer: (B) 4800/x+60
Question: The ratio between the present ages of P and Q is 6:7. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years
(A) 7:8
(B) 7:9
(C) 3:8
(D) 5:8
(E) 6:8
Rationale: Explanation:
Let P age and Q age is 6x years and 7x years.
Then 7x - 6x = 4 <=> x = 4
So required ratio will be (6x+4): (7x+4) => 28:32 => 7:8
Answer: Option A
Answer: (A) 7:8
Question: Pipes A and B can fill a tank in 5 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in:
(A) 3 9 /17 hours
(B) 1 13 /17 hours
(C) 2 8 /11 hours
(D) 4 1 /2 hours
(E) None of these
Rationale: Explanation:
Solution 1
Pipes A and B can fill the tank in 5 and 6 hours respectively. Therefore,
part filled by pipe A in 1 hour =1/5
part filled by pipe B in 1 hour =1/6
Pipe C can empty the tank in 12 hours. Therefore,
part emptied by pipe C in 1 hour =1/12
Net part filled by Pipes A,B,C together in 1 hour =1/5 +1/6+1/12 =17/60
i.e., the tank can be filled in 60/17=3 9/17 hours.
ANSWER IS A
Answer: (A) 3 9 /17 hours
Question: Simple interest on a certain sum is 9.8 over 20 of the sum. Find the rate per cent and time, if both are equal.
(A) 7% and 7 years
(B) 6% and 6 years
(C) 10% and 10 years
(D) 12 % and 12 years
(E) None of these
Rationale: 9.8â„20 P = PÃ—RÃ—R/100
â‡’ R2 = 980â„20=49 â‡’ R = 7%
Also, time = 7 years
Answer A
Answer: (A) 7% and 7 years
Question: An businessman earns an income of Re 2 on the first day of his business. On every subsequent day, he earns an income which is just double of that made on the previous day. On the 20th day of business, he earns an income of:
(A) 21
(B) 22
(C) 36
(D) 20
(E) 30
Rationale: 2nd day he earns = 2(2 – 2)
3rd day he earns = 2(3 – 2)
On 20th day he earns 2(20 -2) = 36 rupees
ANSWER:C
Answer: (C) 36
Question: Walking 6/7th of his usual speed, a man is 12 minutes too late. The usual time taken by him to cover that distance is :
(A) 1 hr 20 min
(B) 1 hr 10 min
(C) 1 hr 11 min
(D) 1 hr 12 min
(E) None
Rationale: Sol.
New speed = 6/7 of usual speed.
New time = 7/6 of usual time
∴ [7/6 of usual time] - (usual time) = 1/5 hr.
⇒ 1/6 of usual time = 1/5 hr ⇒ usual time = 6/5 hr = 1 hr 12 min.
Answer D
Answer: (D) 1 hr 12 min
Question: Raju age after 25 years will be 5 times his age 5 years back, What is the present age of Raju
(A) 28
(B) 17
(C) 10.21
(D) 77
(E) 12.5
Rationale: Clearly,
x+25 = 5(x-5)
<=> 4x = 50 => x = 12.5
Answer:E
Answer: (E) 12.5
Question: What is the least integer that is a sum of four different prime numbers each greater than 10?
(A) 60
(B) 62
(C) 64
(D) 66
(E) 68
Rationale: The sum of the four smallest primes greater than 10 is 11+13+17+19=60.
The answer is A.
Answer: (A) 60
Question: At Company K, 15 percent of the employees are secretaries and 60 percent are salespeople. If there are 55 other employees of Company K, how many employees does Company K have?
(A)  160
(B)  180
(C)  190
(D)  200
(E)  220
Rationale: Let the total number of employees in the company be x
% of secretaries = 15%
% of salespeople = 60%
% of of employees other than secretaries and salespeople = 100 - 75 = 25%
But this number is given as 55
so 25% of x = 55
x = 220
Therefore there a total of 220 employees in the company K
Correct answer - E
Answer: (E)  220
Question: If you divide 7^93 by 5, which remainder do you get?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: The units digit of 7^1 is 7.
The units digit of 7^2 is 9.
The units digit of 7^3 is 3.
The units digit of 7^4 is 1.
The units digit of 7^5 is 7.
etc...
The units digit of 7^n repeats in blocks of 4: {7, 9, 3, 1}
The remainder of 93/4 is 1.
So the units digit of 7^93 is 7.
The remainder of 7^93 / 5 is 2.
The answer is C.
Answer: (C) 2
Question: An athlete runs 200 meters race in 18sec. His speed is?
(A) 20km/hr
(B) 15km/hr
(C) 30km/hr
(D) 25km/hr
(E) 40km/hr
Rationale: speed = 200/18 = 100/9 m/sec
= 100/9 * 18/5 km/hr = 40km/hr
Answer is E
Answer: (E) 40km/hr
Question: The number of roots common between the two equations x3+3x2+4x+5=0x3+3x2+4x+5=0 and x3+2x2+7x+3=0x3+2x2+7x+3=0 is
(A) 22
(B) 27
(C) 13
(D) 88
(E) 21
Rationale: Here f(x) = x3+3x2+4x+5=0x3+3x2+4x+5=0 and g(x) = x3+2x2+7x+3=0x3+2x2+7x+3=0
To find the common roots we have to solve the equation f(x) - g(x) = 0
i.e. (x3+3x2+4x+5)(x3+3x2+4x+5) - (x3+2x2+7x+3)=0(x3+2x2+7x+3)=0
x2−3x+2=0x2−3x+2=0
x = 2, x = 1
These are the points of intersection f(x) and g(x). Whether these points are also the common root will have to be checked by putting these vales in f(x) = 0 and g(x) = 0.
For x = 2;
f(2) = g(2) = 43 ≠≠ 0. Hence 2 is not a common root but only a point of intersection.
For x = 1;
f(1) = g(1) = 13 ≠≠ 0. Again 1 is not a common root but a point of intersection. Hence, we find that the two equations do not have any common root between them.
Answer:C
Answer: (C) 13
Question: If a quality control check is made inspecting a sample of 2 light bulbs from a box of 8 lighbulbs, how many different samples can be chosen?
(A) 6
(B) 28
(C) 36
(D) 66
(E) 72
Rationale: Try using the formula for combinations:
n!/r!(n-r)!
8!/2!(8-2)!
8!/2!*6!
8*7/2*1
=28
B
Answer: (B) 28
Question: A boy want to make a cuboid of dimension 5m, 6m, 7m from small cubes of .04 m3. Later he realized he can make same cuboid by making it hollow. Then it takes some cubes less. What is the no. of these cubes?
(A) 2150
(B) 2250
(C) 2350
(D) 2850
(E) 3250
Rationale: volume of cuboid=5*6*7=210m3
volume of inner cuboid=(5-1)*(6-1)*(7-1)=120m3
therefore,volume of hollow cuboid=210-120=90 m3
no of cubes required=90/.04=2250 cubes
ANSWER:B
Answer: (B) 2250
Question: If X,Y is 20%,25% greater than Z then how much percentage is X smaller than Y?
(A) 2
(B) 4
(C) 6
(D) 7
(E) 1
Rationale: X=120%
Y=125%
Z=100%
X-Y/Y*100 = 5/125*100
==>4%
ANSWER B
Answer: (B) 4
Question: A data set with a mean of 60 has a standard deviation of 8.7. Which of the following is the smallest number that falls within one standard deviation of the mean?
(A) 51
(B) 56
(C) 59
(D) 63.5
(E) 65
Rationale: One standard deviation of the mean is from{mean}-{deviation}=60-8.7=51.3 to{mean}+{deviation}=60+8.7=68.7. The smallest number within this range from the options is 51.
Answer: A.
Hope this helps.
Answer: (A) 51
Question: Anne traveled from City A to City B in 4 hours, and her speed was between 20 miles per hour and 40 miles per hour. John traveled from City A to City B along the same route in 2 hours, and his speed was between 45 miles per hour and 60 miles per hour. Which of the following could be the distance, in miles, from City A to City B?
(A) 95
(B) 115
(C) 125
(D) 160
(E) 180
Rationale: In four hours Anne must travel 4 times her speed
so Anne's possible distances =
4(20 -40) or 80-160 miles
in two hours John travels 2 times his speed or
2(45-60) or 90-120 miles
the statement is only true if both distances are possible,
so you can tell its between or equal to
90-120
B is the answer.
Answer: (B) 115
Question: At the time of marriage, a man was 6 years elder to his wife. 14 years after their marriage, his age is 8/7 times the age of his wife. What was wife's age at the time of marriage ? Choose one answer.
(A) 36 years
(B) 30 years
(C) 28 years
(D) 14 years
(E) 26 years
Rationale: let wifes age= x
husband age = x+6
now after 14 years of mrg x+14 wifes age
x+6+14 husbands age
8/7(x+14)=x+6+14
after solving x=28
ANSWER:C
Answer: (C) 28 years
Question: g(a) is defined as the product of all even integers k such that 0 < k ≤ x. For example, g(14) = 2 × 4 × 6 × 8 × 10 × 12 × 14. If g(y) is divisible by 4^11, what is the smallest possible value for a?
(A)  22
(B)  24
(C)  28
(D)  32
(E)  44
Rationale: g(a)=4^11=2^22. So we have to find a product with atleast 22 2's in it.
in option 1 22 the total no of 2's = [22/2] + [22/4] +[22/8] +[22/16] = 11+5+2+1 = 19
in option 2 24 the total no of 2's = [24/2] + [24/4] +[24/8] +[24/16] = 12+6+3+1 = 22 . Hence B
Answer: (B)  24
Question: A merchant has 1000 kg of sugar part of which he sells at 8% profit and the rest at 18% profit. He
gains 14% on the whole. The Quantity sold at 18% profit is
(A) 300
(B) 400
(C) 600
(D) 500
(E) None of these
Rationale: Explanation :
By the rule of alligation,we have
Profit% by selling 1st part Profit% by selling 2nd part
8 18
Net % profit
14
18-14=4 14-8=6
=> Quantity of part1 : Quantity of part2 = 4 : 6 = 2 : 3
Total quantity is given as 1000Kg
So Quantity of part2 (Quantity sold at 18% profit) = 1000×35=600Kg
Answer : Option C
Answer: (C) 600
Question: A train 960 m long passed a pole in 24 sec. How long will it take to pass a platform 800 m long?
(A) 40
(B) 44
(C) 48
(D) 52
(E) 56
Rationale: Speed = 960/24
= 40 m/sec.
Required time
= (960 + 800)/40
= 44 sec.
Answer:B
Answer: (B) 44
Question: All the students of class are told to sit in circle shape. Here the boy at the 6 th position is exactly opposite to 16 th boy. Total number of boys in the class?
(A) 10
(B) 15
(C) 20
(D) 25
(E) 30
Rationale: As half the circle shape consist of 16-6=10 boys,
So total number of boys in full circle=2*10=20
ANSWER:C
Answer: (C) 20
Question: The speed of a boat in upstream is 75 kmph and the speed of the boat downstream is 115 kmph. Find the speed of the boat in still water and the speed of the stream?
(A) 20 kmph
(B) 76 kmph
(C) 12 kmph
(D) 97 kmph
(E) 15 kmph
Rationale: Speed of the boat in still water
= (75+115)/2
= 90 kmph. Speed of the stream
= (115-75)/2
= 20 kmph.
Answer:A
Answer: (A) 20 kmph
Question: Data sufficiency question:
There are six people. Each cast one vote in favor of other five. Who won the elections?
i) 4 older cast their vote in favor of the oldest candidate
ii) 2 younger cast their vote to the second oldest
(A) 287
(B) 27
(C) 199
(D) 17
(E) 191
Rationale: xplanation:
Total possible votes are 6. Of which 4 votes went to the oldest person. So he must have won the election. Statement 1 is sufficient.
Answer:D
Answer: (D) 17
Question: A committee has 5 men and 6 women. What are the number of ways of selecting 2 men and 3 women from the given committee?
(A) 187
(B) 200
(C) 827
(D) 289
(E) 270
Rationale: The number of ways to select two men and three women
= ⁵C₂ * ⁶C₃
= (5 *4 )/(2 * 1) * (6 * 5 * 4)/(3 * 2)
= 200
Answer:B
Answer: (B) 200
Question: What is the smallest positive integer x such that 864x is the cube of a positive integer
(A) 6
(B) 12
(C) 9
(D) 5
(E) 2
Rationale: Given 864x is a perfect cube
so we will take 1728= 12*12*12
864x = 1728
x =1728/864= 2
correct option is E
Answer: (E) 2
Question: The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 12 units?
(A) 140
(B) 99
(C) 88
(D) 72
(E) 168
Rationale: Given that the area of the square = 1225 sq.units
=> Side of square = √1225 = 35 units
The radius of the circle = side of the square = 35 units Length of the rectangle = 2/5 * 35 = 14 units
Given that breadth = 12 units
Area of the rectangle = lb = 14 * 12 = 168 sq.units
Answer: E
Answer: (E) 168
Question: A is twice as good a work man as B and together they finish a piece of work in 24 days.The number of days taken by A alone to finish the work is :
(A) 28 days.
(B) 16 days.
(C) 12 days.
(D) 24 days.
(E) 36 days.
Rationale: Solution
(A’s 1 day’s work): (B’s 1 day’s work)= 2 : 1.
(A + B)'s 1 day’s work = 1/24
Divide 1/14 in the ratio 2 : 1.
∴ A’s 1 day’s work = (1/24 x2/3)= 1/36
Hence,A alone can finish the work in 36 days.
Answer E
Answer: (E) 36 days.
Question: For a particular American football game, the probability of a team's quarterback throwing a completed pass on each throw is 3/10. What is the least number of times that the quarterback should throw the ball that will increase the probability of getting a completed pass at least once to more than 50%.
(A) 10
(B) 5
(C) 2
(D) 3
(E) 1
Rationale: Rule of Subtraction: P(A) = 1 - P(A')
Rule of Multiplication: P(A ∩ B) = P(A) P(B)
The probability that the quarterback throws a completed pass at least once in 2 throws is 1- (7/10)^2 = 1 - 49/100 = 51/100 > 50%
Answer: C
Answer: (C) 2
Question: If x and y are multiples of 2 then which are all the multiples of 2
1) x*y
2) x^y
3) x+y
4) x-y
5) x/y
(A) 1,3
(B) 1,2,4,5
(C) 1,2,5
(D) 1,2,3,4
(E) all of these
Rationale: x*y,x^y,x+y, x-Y are even numbers
ANSWER:D
Answer: (D) 1,2,3,4
Question: A father was as old as his son's present at the time of your birth. If the father's age is 38 years now, the son's age 5years back was?
(A) 10 years
(B) 12 years
(C) 14 years
(D) 16 years
(E) 18 years
Rationale: Let the son's present age be x years. Then, (38 - x) = x
2x = 38.
x = 19.
Son's age 5 years back (19 - 5) = 14 years.
C
Answer: (C) 14 years
Question: what is the sum of the first 30 odd natural numbers
(A) 300
(B) 400
(C) 900
(D) 600
(E) 700
Rationale: sum of first n odd natural nuber is = n^2
so sum of the first 30 odd natural numbers=(30)^2=900
ans 900
ANSWER:C
Answer: (C) 900
Question: How many times digit 10 is used while writing numbers from 100 to 1000?
(A) 100
(B) 90
(C) 85
(D) 110
(E) 120
Rationale: in 100 to 300 there are 20 ten's
in 300 to 500 there are 20 ten's
in 500 to 700 there are 20 ten's
in 700 t0 900 there are 20 ten's
in 900 to 1000 there are 10 ten's
so total is 90 ten's
CORRECT OPTION :B
Answer: (B) 90
Question: Workers at a campaign office have 3000 fliers to send out. If they send out 1/5 of them in the morning and 1/4 of the remaining ones out during the afternoon, how many are left for the next day?
(A) 1800
(B) 800
(C) 1100
(D) 1200
(E) 1900
Rationale: (1/5)*3000 = 600
Remaining = 3000-600 = 2400
(1/4) of remaining = (1/4)*2400 = 600
Remaining now = 2400-600 = 1800
Answer: Option A
Answer: (A) 1800
Question: Arun went for a movie nine days ago. He goes to watch movies only on Thursdays. What day of the week is today?
(A) Wednesday
(B) Saturday
(C) Friday
(D) Sunday
(E) Monday
Rationale: Explanation:
Clearly it can be understood from the question that 9 days ago was a Thursday
Number of odd days in 9 days = 2 (As 9-7 = 2, reduced perfect multiple of 7 from total days)
Hence today = (Thursday + 2 odd days) = Saturday
Answer: Option B
Answer: (B) Saturday
Question: By selling 12 toffees for a rupee, a man loses 20%. How many for a rupee should be sell to get a gain of 20%?
(A) 7
(B) 8
(C) 9
(D) 6
(E) 4
Rationale: Let S.P. of 12 toffees be Rs. x.
Then, 80:1 = 120:x or x = 120/180 = 3/2
For Rs. 3/2, toffees sold = 12.
For Re. 1, toffees sold = 12 * 2/3 = 8
Answer: B
Answer: (B) 8
Question: When working alone, painter W can paint a room in 2 hours, and working alone, painter X can paint the same room in f hours. When the two painters work together and independently, they can paint the room in 3/4 of an hour. What is the value of f?
(A) 3/4
(B) 1[1/5]
(C) 1[2/5]
(D) 1[3/4]
(E) 2
Rationale: Rate*Time=Work
Let Painter W's rate be W and Painter X's rate be X
R*T = Work
W * 2 = 1 (If the work done is same throughout the question then the work done can be taken as 1) => W = 1/2
X * f = 1 => X = 1/f
When they both work together then their rates get added up
Combined Rate = (W+X)
R*T = Work
(W+X) * 3/4 = 1
=> W+X = 4/3
=> 1/2 + 1/f = 4/3
=> 1/f = (8-3)/6 = 5/6
=> f = 6/5 = 1[1/5]
Answer B
Answer: (B) 1[1/5]