mathewhe/aqua_rat huggingface dataset:
Question: A coin is tossed four times. What is the probability that there is at the least one tail?
(A) 15/16
(B) 31/37
(C) 31/18
(D) 31/10
(E) 31/19
Rationale: Let P(T) be the probability of getting least one tail when the coin is tossed four times.
= There is not even a single tail.
i.e. all the outcomes are heads.
= 1/16 ; P(T) = 1 - 1/16 = 15/16
Answer: A
Answer: (A) 15/16
Question: If a randomly selected positive single digit multiple of 3 is multiplied by a randomly selected prime number less than 20, what is the probability Q that this product will be a multiple of 45?
(A) 1/32
(B) 1/28
(C) 1/24
(D) 1/16
(E) 1/14
Rationale: There are 3 single digit multiple of 3, that is, 3,6,9.
There are 8 prime nos less than 20 - 2,3,5,7,11,13,17,19
Total outcome - 8*3 = 24
Favourable outcome = 1 (9*5)
Hence required probability Q= 1/24. Answer C.
Answer: (C) 1/24
Question: A train moving at 2/3 rd of its normal speed reaches its destination 20 minutes late. Find the normal time taken?
(A) 1 hour
(B) 1/3 hour
(C) 2/3 hour
(D) 3/4 hour
(E) 1/4 hour
Rationale: Let the original speed and time is S and T
then distance =S*T
Now the speed changes to 2/3S and T is T+20
As the distance is same
S*T=2/3S*(T+20)
solving this we get t=40 minutes
=40/60=2/3 hour
ANSWER:C
Answer: (C) 2/3 hour
Question: Convert the 17/36 m/s into kilometers per hour?
(A) 1.7
(B) 1.5
(C) 1.3
(D) 1.1
(E) 1.2
Rationale: 17/36 m/s = 17/36 * 18/5 = 17/10
= 1.7 kmph.
Answer: A
Answer: (A) 1.7
Question: A bar over a sequence of digits in a decimal indicates that the sequence repeats indefinitely. What is the value of (10^4 -10^2)(0.0017)?
(A) 14.83
(B) 17.83
(C) 18.83
(D) 16.83
(E) 26.83
Rationale: You get 10^2 (100-1) (.0017)
we know 17/10000 = .0017
10^2 (99) * (17/10000)
10^2 = 100 and 100^2 = 10000
Cancel out the 100 with the 10^2
Left with 99(17/100).
0.99*17 = 16.83
Answer : D
Answer: (D) 16.83
Question: If x + y = 6 and x – y = 3, then x^2 - y^2 =
(A) -4
(B) 4
(C) 10
(D) 19
(E) 40
Rationale: The fastest approach has already been shown. Here's one more option.
Given:
x + y = 6
x – y = 3
Add the two equations to get: 2x = 9, which means x = 4.5
If x = 4.5, we can plug that value into either equation, to conclude that y = 1.5
If x = 4.5 and y = 1.5, then x² - y² = 4.5² - 1.5² = 19
Answer: D
Answer: (D) 19
Question: P beats Q by 125 meter in a kilometer race. Find Q's speed if P's speed is 8 meter/sec.
(A) 12.25 meter/sec
(B) 7 meter/sec
(C) 14 meter/sec
(D) 18 meter/sec
(E) 28 meter/sec
Rationale: P's speed = 8 m/s
P's distance = 1000 m (as it is a km race)
t = 1000/8 = 125 sec
Q's distance = 1000-125= 875m
Q's time to complete this distance is also 62.5 sec.
Q's speed = dist/time = 875/125 = 7 m/s
Hence B is the answer.
Answer: (B) 7 meter/sec
Question: How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length?
(A) 12.7 sec
(B) 12.1 sec
(C) 18.1 sec
(D) 17.1 sec
(E) 12.7 sec
Rationale: Speed = 72 * 5/18
= 20 m/sec
Total distance covered
= 110 + 132 = 242 m.
Required time = 242/20 '
= 12.1 sec.
Answer:B
Answer: (B) 12.1 sec
Question: A train 600m long is running at 54km/hr. How much time will it take to cross a pole?
(A) 30 secs.
(B) 42 secs.
(C) 35 secs.
(D) 45 secs.
(E) 40 secs.
Rationale: Distance covered =600m =3/5km speed =54km/hr. Time =3/5*54 =1/90hrs. =1/90*3600 =40 secs. Answer : E
Answer: (E) 40 secs.
Question: The S.I. on a certain sum of money for 6 years at 16% per annum is half the C.I. on Rs. 8000 for 2 years at 20% per annum. The sum placed on S.I. is?
(A) 3000.33
(B) 2802.33
(C) 1833.33
(D) 2990.33
(E) 2982.33
Rationale: C.I. = [8000 * (1 + 20/100)2 - 8000]= (8000 * 6/5 * 6/5 - 8000) = Rs. 3520.Sum = (3520 * 100)/(6 * 16)= Rs.1833.33Answer:C
Answer: (C) 1833.33
Question: In how many ways can a cricket eleven be chosen out of a batch of 15 players.
(A) 1784
(B) 4561
(C) 1450
(D) 1365
(E) 1250
Rationale: Required number of ways
= 15C 11 = 15C (15-11)
= 15 C 4
15C4 = 15 * 14 * 13 * 12 / 4 * 3 * 2 *1
= 1365
Ans: D
Answer: (D) 1365
Question: Ramesh purchased a refrigerator for Rs. 16500 after getting a discount of 20% on the labelled price. He spent Rs. 125 on transport and Rs. 250 on installation. At what price should it be sold so that the profit earned would be 10% if no discount was offered?
(A) 34778
(B) 26888
(C) 22899
(D) 23100
(E) 32778
Rationale: Price at which the TV set is bought = Rs. 16,500
Discount offered = 20%
Marked Price = 16500 * 100/80 = Rs. 20625
The total amount spent on transport and installation = 125 + 250 = Rs. 375\Total price of TV set = 20625 + 375 = Rs. 21000
The price at which the TV should be sold to get a profit of 10% if no discount was offered = 21000 * 110/100
= Rs. 23100
Answer: D
Answer: (D) 23100
Question: There are 7 players in a bowling team with an average weight of 94 Kg. If two new players join the team, one weighs 110 Kg and the second weighs 60 Kg, what will be the new average weight?
(A) 75 Kg.
(B) 80 Kg.
(C) 86 Kg.
(D) 90 Kg.
(E) 92 Kg.
Rationale: The New average will be= (94*7+110+60)/9= 92 kgs
E is the answer
Answer: (E) 92 Kg.
Question: In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 75 questions and secures 125 marks, the number of questions he attempts correctly, is :
(A) 38
(B) 40
(C) 26
(D) 25
(E) 11
Rationale: Explanation:
Let the number of correct answers be x.
Then numbers of incorrect answers will be 75 – x
We get 4x – (75 – x)×1= 125
On solving the equation we get x= 40
Answer: B
Answer: (B) 40
Question: 3889 + 12.952 – ? = 3854.002
(A) 47.095
(B) 47.752
(C) 47.932
(D) 47.95
(E) None of these
Rationale: Solution
Let 3889 + 12.952 - x = 3854.002.
Then, x = (3889 + 12.952) - 3854.002 = 3901.952 - 3854.002 = 47.95. Answer D
Answer: (D) 47.95
Question: A satellite is composed of 24 modular units, each of which is equipped with a set of sensors, some of which have been upgraded. Each unit contains the same number of non-upgraded sensors. If the number of non-upgraded sensors on one unit is 1/4 the total number of upgraded sensors on the entire satellite, what fraction of the sensors on the satellite have been upgraded?
(A) 5/6
(B) 1/5
(C) 1/6
(D) 1/7
(E) 1/24
Rationale: Let x be the number of upgraded sensors on the satellite.
The number of non-upgraded sensors per unit is x/4.
The number of non-upgraded sensors on the whole satellite is 24(x/4) = 6x.
The fraction of sensors which have been upgraded is x / (x+6x) = x/7x = 1/7
The answer is D.
Answer: (D) 1/7
Question: In a two-digit number, if it is known that its unit's digit exceeds its ten's digit by 2 and that the product of the given number and the sum of its digits is equal to 280, then the number is:
(A) 16
(B) 24
(C) 27
(D) 35
(E) 46
Rationale: Let the ten's digit be x. Then, unit's digit = x + 2. Number = 10x + (x + 2) = 11x + 2
Sum of digits = x + (x + 2) = 2x + 2
(11x + 2)(2x + 2) =280
22(x)(x) + 26x - 276 = 0
11(x)(x) + 13x -138 = 0
(x - 3)(11x + 46) = 0
x = 3
Hence, required number = 11x + 2 = 35.
ANSWER:D
Answer: (D) 35
Question: A cargo ships engines failed 100 miles away from the port. Due to the changing wind direction, it is moving 12 miles towards the port and 6 miles away from the port. If the wind pattern remains same, how many miles it will travel before reaching the port?
(A) A - 179
(B) B - 240
(C) C - 280
(D) D - 100
(E) E - 155
Rationale: Ships overall distance covered per cycle is +6 miles
take 100 - 6
take 94/6 to lowest divisible number - 90/6
This means that it will take 15 "overall" actions to reach the 90th mile. -15*18 miles added later
Set cycle start at 90. travel 10 miles and reach the anchor point - add 10 to total
15*18 + 10 = 280 miles in total
Answer: C
Answer: (C) C - 280
Question: If m=4p where p is a prime number greater than 2, how many different positive even divisors does m have, including m?
(A) two
(B) three
(C) four
(D) six
(E) eight
Rationale: m=2, 2, p (p is in the prime factorization since were told it is a prime number in the question)
2
4 (because of 2*2)
2p (because of 2 * p)
4p (because of 2 * 2 * p)=C
Answer: (C) four
Question: Ramu bought an old car for Rs. 45000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent?
(A) A)12.5%
(B) B)16%
(C) C)18%
(D) D)22%
(E) of these
Rationale: Total CP = Rs. 45000 + Rs. 13000 = Rs. 58000 and SP = Rs. 64900
Profit(%) = (64900 - 58000)/55000 * 100 = 18%
ANSWER:A
Answer: (A) A)12.5%
Question: Two pipes A and B can fill a cistern in 12 and 15 minutes respectively. Both are opened together but after 6 minutes A is turned off. After how much more time will the cistern be filled?
(A) 8 1/7
(B) 8 1/1
(C) 8 1/4
(D) 1 1/2
(E) 8 3/7
Rationale: 6/12 + (6 + x)/15 = 1
x = 1 1/2
Answer: D
Answer: (D) 1 1/2
Question: What is the place value of 4 in the numeral 2436?
(A) 400
(B) 500
(C) 700
(D) 800
(E) 840
Rationale: Option 'A'
4 * 100 = 400
Answer: (A) 400
Question: The sum of how many terms of the series 6 + 12 + 18 + 24 + ... is 1800 ?
(A) 20
(B) 24
(C) 28
(D) 32
(E) 24
Rationale: This is an A.P. in which a = 6, d = 6 and Sn = 1800
Then, n [2a + (n - 1)d] = 1800
2
n [2 x 6 + (n - 1) x 6] = 1800
2
3n (n + 1) = 1800
n(n + 1) = 600
n2 + n - 600 = 0
n2 + 25n - 24n - 600 = 0
n(n + 25) - 24(n + 25) = 0
(n + 25)(n - 24) = 0
n = 24
Number of terms = 24.
B)
Answer: (B) 24
Question: what is the 49 th word if the letters of the word ABUSER is arranged in alphabetical order
(A) ARBESV
(B) ARBESW
(C) ARBESU
(D) ARBESS
(E) ARBESE
Rationale: Firstly arrange it in alphabatical order i.e
ABERSU
Take first two letter as a constant i.e ABersu
(remaining ersu can be arranged in 4! ways)
the next letter according to dictionary is AEbrsu take first two letter as a constant i.e AEbrsu(remaining brsu can be arranged in 4! ways)
when AB constant no of words will formed = 24
when AE constant no of words will formed = 24
so far we had completed 48 words the
49 word is ARBESU
ANSWER:C
Answer: (C) ARBESU
Question: Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is:
(A) 228gallons
(B) 267gallons
(C) 120gallons
(D) 767gallons
(E) 167gallons
Rationale: Explanation:
Work done by the waste pipe in 1 minute ={\color{Black} \frac{1}{15}-\left ( \frac{1}{20}+\frac{1}{24} \right )=\left ( \frac{1}{15}-\frac{11}{120} \right )=-\frac{1}{40}} [-ve sign means emptying]
Volume of {\color{Black} \frac{1}{40}} part = 3 gallons
Volume of whole = (3 x 40) gallons = 120 gallons.
Answer: C
Answer: (C) 120gallons
Question: A salt manufacturing company produced a total of 1000 tonnes of salt in January of a particular year. Starting from February its production increased by 100 tonnes every month over the previous months until the end of the year. Find its ave66rage daily production for that year?
(A) 51
(B) 53
(C) 55
(D) 56
(E) 57
Rationale: Total production of salt by the company in that year = 1000 + 1100 + 1200 + .... + 2100 = 18600.
Average monthly production of salt for that year = 18600/365 â‰ˆ 51
ANSWER:A
Answer: (A) 51
Question: By looking at a rectangular box, a carpenter estimates that the length of the box is between 2 to 2.1 meters, inclusive, the breadth is between 1 to 1.1 meters, inclusive and the height is between 2 to 2.1 centimeters, inclusive. If the actual length, breadth and height of the box do indeed fall within the respective ranges estimated by the carpenter, which of the following is the closest to the maximum possible magnitude of the percentage error R that the carpenter can make in calculating the volume of the rectangular box?
(A) 1%
(B) 3%
(C) 10%
(D) 18%
(E) 22%
Rationale: the dimensions are between 2-2.1, 1-1.1 and 2-2.1..
so MAX error in Volume=?..
IMPORTANT POINTS TO NOTE
1) Max ERROR would be when actuals and estimate are at the extreme ends..
2) BUT what about MAX % ERROR--
It will be when the base is the lowest...
so the ACTUALS should be lowest or at lower end and the ESTIMATE at the higher end..
SOLUTION
Actuals= 2*2*1=4..
Estimate=2.1*2.1*1.1=4.841..
Max % error R=(4.841-4)/4 *100= 84.1/4 = 21.25%..
21.25% is closest to 22% in the choices..
ans E
Answer: (E) 22%
Question: A theater box office sold an average (arithmetic mean) of 64 tickets per staff member to a particular movie. Among the daytime staff, the average number sold per member was 76, and among the evening staff, the average number sold was 60. If there are no other employees, what was the ratio of the number of daytime staff members to the number of evening staff members?
(A) 2:5
(B) 1:4
(C) 1:3
(D) 15:19
(E) 64:76
Rationale: Deviation from the mean for the daytime staff = 76 - 64 = 12.
Deviation from the mean for the evening staff = 64 - 60 = 4.
Thus, the ratio of the number of daytime staff members to the number of evening staff members is 4:12 = 1:3.
The answer is C.
Answer: (C) 1:3
Question: The speed of a car is 80 km in the first hour and 40 km in the second hour. What is the average speed of the car?
(A) 72 kmph
(B) 60 kmph
(C) 30 kmph
(D) 80 kmph
(E) 82 kmph
Rationale: S = (80 + 40)/2
= 60 kmph
ANSWER:B
Answer: (B) 60 kmph
Question: According to the formula F=9/5 (C) +32, if the temperature in degrees Farenheit (F) increases by 25, by how much does the temperature in degrees Celsius (C) increase?
(A) 9
(B) 13.88
(C) 47
(D) 48 3/5
(E) 59
Rationale: You can plug in values.
C = 5/9*(F-32)
F=32 --> C=0;
F=32+25=57 --> C=5/9*25=13.88.
Increase = 13.88 degrees.
Answer: B.
Answer: (B) 13.88
Question: Initially, the men and women in a room were in the ratio of 4 : 5. Then, 2 men entered the room and 3 women left the room. Then, the number of women doubled. Now there are 14 men in the room. How many Q women are currently in the room?
(A) 12
(B) 14
(C) 15
(D) 24
(E) 36
Rationale: the number of women doubled means that they have become 24 from 12..
and we have to tell the current strength so 24 is the answer..
let the number be 4x and 5x..
given 4x+2=14.. so x=3..
women number Q =5*3-3=12, then doubled=24..
ans D
Answer: (D) 24
Question: A, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain be Rs.19200. A's share is?
(A) 8876
(B) 2765
(C) 6400
(D) 1298
(E) 1261
Rationale: x* 12 : 2x* 6: 3x* 4
1:1:1
1/3 * 19200 = 6400
Answer:C
Answer: (C) 6400
Question: Nine persons went to a hotel for taking their meals. Eight of them spent 12 each on their meals and the ninth spend 8 more than the average expenditure of all the nine. What was the total money spent by them?
(A) 115
(B) 117
(C) 119
(D) 122
(E) None of the above
Rationale: Let the average expenditure of all the nine be x.
Then, 12 × 8 + (x + 8) = 9x or 8x = 104 or x = 13.
∴ Total money spent = 9x = (9 × 13) = 117.
Answer B
Answer: (B) 117
Question: If John takes 11 minutes to eat x raisins, how many seconds will it take him to eat z raisins, assuming he continues to eat at the same rate?
(A) 660x/z
(B) 11x/z
(C) 660xz
(D) 660z/x
(E) 11z/x
Rationale: It will take (z/x)(11) minutes which is (z/x)(11)(60) seconds = 660z/x seconds.
The answer is D.
Answer: (D) 660z/x
Question: In a hostel there were 100 students. To accommodate 25 more students the average is decreased by rupees 10. But total expenditure increased by Rs.500. Find the total expenditure of the hostel now?
(A) 7500
(B) 5000
(C) 5400
(D) 7000
(E) 8500
Rationale: Let average is x
100x + 500 = 125(x – 10)
x = 70
100 * 70 + 500 = 7500
Answer:A
Answer: (A) 7500
Question: 3889 + 12.998 - ? = 3854.002
(A) A)47.996
(B) B)47.752
(C) C)47.932
(D) D)47.95
(E) of the above
Rationale: Let 3889 + 12.998 - x = 3854.002.
Then x = (3889 + 12.998) - 3854.002
= 3901.998 - 3854.002
= 47.996.
Answer = A
Answer: (A) A)47.996
Question: Jim needs $1,000 to buy a new flat-screen TV. Since he has only $7, he borrows the remaining balance from his sister Mary. The loan will be repaid in 3 annual installments at an interest rate of 10%, compounded annually. The formula for calculating the monthly payment P is P = (L x C x r) / (C – 1) where L = amount of the loan, r = annual interest rate, and C = compounding factor = (1 + r)^N where N = number of annual payments. How much does Jim have to pay Mary at the end of each of the next 3 years (rounded to the nearest penny)?
(A) $357.67
(B) $375.85
(C) $387.40
(D) $399.30
(E) $433.33
Rationale: L = 993
r = 0.1
C = 1.1^3 = 1.331
Insert all of these in the formula and we get
P = 993*1.331*0.1/0.331
In order to resolve above without a calc, we need to find the approx value of 0.1331/0.331 ~ 0.4~
~ 993*0.4
~ 397
Answer D
Answer: (D) $399.30
Question: The difference between the place value and the face value of 7 in the numeral 856973 is
(A) 63
(B) 6973
(C) 5994
(D) 6084
(E) None of these
Rationale: (Place value of 7) - (Face value of 7) = (70 - 7) = 63
Answer: Option A
Answer: (A) 63
Question: Sara is an avid lottery player. In the certain game she plays, she must pick one number between 30 and 39, inclusive, one number between 40 and 49, inclusive, and one number between 50 and 59, inclusive. She believes that she will have the best chance of winning if her three numbers, as a set, have the greatest number of distinct prime factors possible. According to Sara’s theory, which of the following sets of three numbers should she use?
(A) 32−48−52
(B) 33−42−56
(C) 39−40−54
(D) 38−49−51
(E) 36−42−56
Rationale: A: 32 (2 as the only PF), 48 (2 and 3 as PF), 52 ( 2 and 13 and PF) - Distinct Prime Factors as a set = 3 (2, 3, and 13).
B: 33 (11 and 3 as PF), 42 (2,3, and 7 as PF), 56 (2 and 7 as PF) - Distinct Prime Factors as a set = 4 (11, 3, 2, and 7).
C: 39 (3 and 13 as PF), 40 (2 and 5 as PF) and 54 (3 and 2 as PF) - Distinct Prime Factors as a set = 4 (3, 13, 2, and 5)
D: 38 (2 and 19 as PF), 49 (7 only) and 51 (17 and 3 as PF) - Distinct Prime Factors as a set = 5 (2, 19, 7, 3, and 17).
E: 36 (2 and 3 as PF), 42 (2, 3, and 7) and 56 ( 2 and 7 as PF) - Distinct Prime Factors as a set = 3 (2, 3, 7)
Answer D.
Answer: (D) 38−49−51
Question: Length of a rectangular plot is 20 mtr more than its breadth. If the cost of fencin gthe plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr?
(A) 50 m
(B) 60 m
(C) 80 m
(D) 82 m
(E) 84 m
Rationale: Let breadth = x metres.
Then, length = (x + 20) metres.
Perimeter = 5300 m = 200 m.
26.50
2[(x + 20) + x] = 200
2x + 20 = 100
2x = 80
x = 40.
Hence, length = x + 20 = 60 m
B
Answer: (B) 60 m
Question: The measures of the 2 acute angles of a triangle are in the ratio of 3 : 7. What arethe measures of the 2 angles?
(A) 20°
(B) 70°
(C) 110°
(D) 63°
(E) 140°
Rationale: If the ratio of the two angles is 3:7, then the measures of two angles can be written as 3x and 7x. Also the two acute angles of a triangle is equal to 90°. Hence
3x + 7x = 90
10x = 90
x = 9
Measures of the two acute angles are
3x = 3 × 9 = 27°
7x = 7 × 9 = 63°
D
Answer: (D) 63°
Question: In how many years will a sum of money doubles itself at 10% per annum on simple interest?
(A) 70%
(B) 20%
(C) 10%
(D) 28%
(E) 20%
Rationale: P = (P*10*R)/100
R = 10%
Answer:C
Answer: (C) 10%
Question: If positive integer n is divisible by both 5 and 16, then n must be divisible by which of the following?
(A) 8
(B) 12
(C) 18
(D) 24
(E) 48
Rationale: A number divisible by both 5,16 is 80 which s divisible by 8.
IMO : Answer A 8
Answer: (A) 8
Question: What is the difference between the place value and face value of 3 in the numeral 1375?
(A) 297
(B) 300
(C) 310
(D) 320
(E) 322
Rationale: place value of 3 = 3 * 100 = 300
face value of 3 = 3
300 - 3 = 297
A
Answer: (A) 297
Question: A train 125 m long passes a man, running at 4 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?
(A) 65 km/hr
(B) 17 km/hr
(C) 76 km/hr
(D) 49 km/hr
(E) 15 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 - 4) km/hr.
x - 4 = 45 => x = 49 km/hr.
Answer: D
Answer: (D) 49 km/hr
Question: A certain car averages 25 miles per gallon of gasoline when driven in the city and 40 miles per gallon when driving on the highway. According to these rates, which of the following is closest to the number of miles per gallon that the car averages when it is driven 10 miles in the city and then 40 miles on the highway?
(A) 28
(B) 30
(C) 33
(D) 35
(E) 38
Rationale: 10*1/25 gpm+40*1/40 gpm=1.4 total gallons
50 total miles/1.4 total gallons=35.7 average mpg
D. 35
Answer: (D) 35
Question: A number increased by 30% gives 780. The number is
(A) 250
(B) 400
(C) 450
(D) 600
(E) 520
Rationale: Formula = TOTAL=100% ,INCRESE = "+" DECREASE= "-"
A number means = 100 %
That same number increased by 30 % = 130 %
130 % -------> 780 (130 × 6= 780)
100 % -------> 600 (100 × 6 =600)
D)
Answer: (D) 600
Question: What number comes next?
452, 693, 714, 526, 937, ?
(A) 113
(B) 231
(C) 145
(D) 148
(E) 123
Rationale: C
145
The numbers 45269371 are being repeated in the same sequence.
Answer: (C) 145
Question: In a certain group of 10 developers, 4 developers code only in Python and the rest program in either Ruby on Rails or PHP - but not both. If a developer organization is to choose a 3-member team, which must have at least 1 developer who codes in Python, how many different programming teams can be chosen?
(A) 100
(B) 40
(C) 66
(D) 80
(E) 75
Rationale: Two ways...
1) total ways = 10C3 = 10!/7!3! = 120..
ways without python developer = 6C3= 6!/3!3!=20..
ways of at least ONE python developer = 120-20 =100..
2) ways of selecting ONLY one = 4*6C2 = 4*15 = 60..
ways of selecting ONLY two = 4C2*6C1 = 6*6 = 36..
ways of selecting all three = 4C3 = 4 = 4..
Total = 60+36+4=100...
ANSWER:A
Answer: (A) 100
Question: Given that p is a positive even integer with a positive units digit, if the units digit of p^3 minus the units digit of p^2 is equal to 0, what is the units digit of p +1?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: p is a positive even integer with a positive units digit--> the units digit of p can be 2, 4, 6, or 8 --> only
In order the units digit of p^3 - p^2 to be 0, the units digit of p^3 and p^2 must be the same. i.e 0,1,5 or 6
Intersection of values is 6, thus the units digit of p + 1 is 6 + 1 = 9.
Answer: A.
Answer: (A) 7
Question: P is able to do a piece of work in 15 days and Q can do the same work in 20 days. If they can work together for 4 days, what is the fraction of work left?
(A) 8/15
(B) 9/15
(C) 11/15
(D) 13/17
(E) 15
Rationale: Amount of work P can do in 1 day = 1/15
Amount of work Q can do in 1 day = 1/20
Amount of work P and Q can do in 1 day = 1/15 + 1/20 = 7/60
Amount of work P and Q can together do in 4 days = 4 × (7/60) = 7/15
A)
Fraction of work left = 1 – 7/15= 8/15
Answer: (A) 8/15
Question: In a group of ducks and cows, the total number of legs are 40 more than twice the number of heads. Find the total number of cows.
(A) 12
(B) 14
(C) 16
(D) 18
(E) 20
Rationale: Let the number of ducks be d
and number of cows be c
Then, total number of legs = 2d + 4c = 2(d + 2c)
total number of heads = c + d
Given that total number of legs are 40 more than twice the number of heads
=> 2(d + 2c) = 40 + 2(c + d)
=> d + 2c = 20 + c + d
=> 2c = 20 + c
=> c = 20
i.e., total number of cows = 20
Answer is E.
Answer: (E) 20
Question: A driver covers a certain distance by car driving at 60 km/hr and returns back to the starting point riding on a scooter at 20 km/hr. What was the average speed for the whole journey?
(A) 24 km/h
(B) 26 km/h
(C) 28 km/h
(D) 30 km/h
(E) 32 km/h
Rationale: time 1 = d / 60
time 2 = d / 20
total time = d/60 + d/20 = 4d/60 = d/15
average speed = total distance / total time = 2d / (d/15) = 30 km/h
The answer is D.
Answer: (D) 30 km/h
Question: x, a, z, and b are single digit positive integers. x = ¼ a. z = ¼ b. (10a + b) + (10x + z) could NOT equal
(A) 55
(B) 60
(C) 95
(D) 63
(E) 110
Rationale: 1) firstly we are not given that all are different integers..
2) since each is a positive single digit integer and x=a/4... a can take only 4 and 8 as value, and x can take 1 and 2..
3) same as 2) for b and z.
so in (10a + b) + (10x + z) ..
10a+b can be
44,48,84,88..
10x+z can be
11,12,21,22..
ans D
Answer: (D) 63