divelab/Sys2Bench huggingface dataset:
Question: A rectangular room has the rectangular shaped rug shown as above figure such that the rug’s area is 220 square feet and its length is 12 feet longer than its width. If the uniform width between the rug and room is 12 feet, what is the area of the region uncovered by the rug (shaded region), in square feet?
Options:
A)32
B)1136
C)40
D)1344
E)104
Rationale: Rug's area = 220
which is (x) x (12+x) = 220
so x= 10
rug maintains a uniform distance of 12 feet
so room has dimension 10+24 and 22+24 i.e. 34 and 46
area of room 34x46 = 1564
area covered is 120
so uncovered area is 1564-220=1344 (ANSWER D)
Answer: D
Question: A bank offers 5% C.I. calculated on half-yearly basis . A customer deposits Rs. 1600 each on 1st January and 1st July of a year. At the end of the year, the amount he would have gained by way of interest is?
Options:
A)288
B)121
C)772
D)992
E)212
Rationale: Amount = [1600 * (1 + 5/(2 * 100)2 + 1600 * (1 + 5/(2 * 100)]
= [1600 * 41/40(41/40 + 1)
= [(1600 * 41 * 81)/(40 * 40)] = Rs. 3321.
C.I. = 3321 - 3200 = Rs. 121.
Answer: B
Answer: B
Question: If x + (1/x) = 5, what is the value of T= x^2 + (1/x)^2?
Options:
A)T=21
B)T=22
C)T=23
D)24
E)27
Rationale: Squaring on both sides,
x^2 + (1/x)^2 + 2(x)(1/x) = 5^2
x^2 + (1/x)^2 = 23
Answer: C
Answer: C
Question: In how many ways can an answer key for a quiz be written if the quiz contains 4 true-false questions followed by 2 multiples-choice questions with 4 answer choices each, if the correct answers to all true-false questions cannot be the same?
Options:
A)120
B)190
C)224
D)298
E)256
Rationale: There are 2^4 = 16 possibilities for the true-false answers.
However we need to remove two cases for TTTT and FFFF.
There are 4*4 = 16 possibilities for the multiple choice questions.
The total number of possibilities is 14*16 = 224.
The answer is C.
Answer: C
Question: In a class of 94 students 41 are taking French, 22 are taking German. Of the students taking French or German, 9 are taking both courses. How many students are not enrolled in either course?
Options:
A)6
B)15
C)24
D)33
E)40
Rationale: Formula for calculating two overlapping sets:
A + B - both + NOT(A or B) = Total
so in our task we have equation:
41 (french) + 22 (german) - 9 (both) + NOT = 94
54 + NOT = 94
NOT = 94 - 54 = 40
So answer is E
Answer: E
Question: If the product of two positive integers is 50, which of the following could be the LCM and HCF of the two numbers?
1. LCM 10 : HCF 5
2. LCM 25 : HCF 2
3. LCM 18 : HCF 4
Options:
A)II only
B)I only
C)III only
D)II,III only
E)I,III only
Rationale: Answer : B
Answer: B
Question: A trained covered x km at 40 kmph and another 2x km at 20 kmph. Find the average speed of the train in covering the entire 3x km.
Options:
A)28 kmph
B)26 kmph
C)24 kmph
D)84 kmph
E)74 kmph
Rationale: Total time taken = x/40 + 2x/20 hours
= 5x/40 = x/8 hours
Average speed = 3x/(x/8)
= 24 kmph
Answer:C
Answer: C
Question: The amount of time that three people worked on a special project was in the ratio of 2 to 3 to 4. If the project took 90 hours, how many more hours did the hardest working person work than the person who worked the least?
Options:
A)18 hours
B)22 hours
C)25 hours
D)26 hours
E)20 hours
Rationale: Let the persons be A, B, C.
Hours worked:
A = 2*90/9 = 20 hours
B = 3*90/9 = 30 hours
C = 4*90/9 = 40 hours
C is the hardest worker and A worked for the least number of hours. So the difference is 40-20 = 20 hours.
Answer : E
Answer: E
Question: Find the quotient: 0.63 / 9
Options:
A)0.5
B)0.3
C)0.9
D)0.1
E)0.7
Rationale: 63 / 9 = 7. Dividend contains 2 places decimal.
0.63 / 9 = 0.7
Answer is E.
Answer: E
Question: In a dairy farm, 20 cows eat 10 bags of husk in 40 days. In how many days one cow will eat one bag of husk?
Options:
A)20
B)40
C)80
D)30
E)60
Rationale: One cow eats 10/20=0.5 bags of husk in 40 days. Then, it eats 1 bag in 40/0.5=80 days
Answer: C
Answer: C
Question: At a certain laboratory, chemical substance are identified by an unordered combination of three different colors. If no chemical may be assigned the same three colors as any other, what is the maximum number of substances that can be identified using nine colors?
Options:
A)21
B)35
C)84
D)135
E)210
Rationale: The prompt tells us that substance is identified by an UNORDERED combination of 3 colors and that no chemical may be assigned the same 3 colors as any other chemical.
As an example, a chemical with the colors A/B/C means that the following combinations CANNOT be used by any other chemical:
ABC
ACB
BAC
BCA
CAB
CBA
By extension, the first part of your calculation would be the number of possible substances that could be identified with 9 colors: 9c3 = 84 possible substances
C
Answer: C
Question: HCF of two numbers is 15 and their LCM is 180. If their sum is 105, then the numbers are
Options:
A)30 and 75
B)35 and 70
C)40 and 65
D)45 and 60
E)55 and 70
Rationale: Explanation:
Let the numbers be 15a and 15b. Then,
15a + 15b = 105 or a+ b = 7 .. (i)
LCM = 15ab = 180
ab = 12..(ii)
Solving equations (i) and (ii), we get a=4, b=3
So, the numbers are 15 ×4 and 15 ×3, i.e., 60 and 45
Answer: D
Answer: D
Question: Anna and Carol buy CDs and tapes at a music store that sells each of its CDs for a certain price and each of its tapes for a certain price. Anna spends twice as much as Carol spends, buying three times as many CDs and the same number of tapes. If Carol spends $60.00 on four CDs and five tapes, how much does one tape cost?
Options:
A)$5.00
B)$6.00
C)$12.00
D)$25.00
E)$100.00
Rationale: CD => C
Type => T
Carol: 4C+5T=60
Anna: 12C+5T=120
12C-4C=60
8C=60
C=7.5
4C+5T=60
30+5T=60
5T=30
T=6
Answer is B
Answer: B
Question: A certain stock exchange designates each stock with a 1, 2 or 3 letter code, where each letter is selected from the 12 letters of the alphabet. If the letters may be repeated and if the same letters used in a different order, constitute a different code, how many diff stocks is it possible to designate with these codes?
Options:
A)2000
B)1900
C)1800
D)1884
E)1600
Rationale: Pretty simple actually
Number of 1 letter symbols = 12
Number of 2 letter symbols = 12*12
Number of 3 letter symbols = 12*12*12
The answer is sum of the 3. = 12 +12*12 + 12*12*12 = 12*(1+12+144) =12*157=1884
So the answer is D.
Answer: D
Question: A number exceeds by 25 from its 3/8 part. Then the number is?
Options:
A)40
B)25
C)20
D)30
E)35
Rationale: x â€“ 3/8 x = 25
x = 40
ANSWER A
Answer: A
Question: one out of five employees are capable of doing a certain task. 50 percent of the five employees, including the one who are capable, are assigned to a project involving this task. what percentage of employees assigned to the project are not capable?
Options:
A)43.33%
B)33.33%
C)50%
D)38.33%
E)23.33%
Rationale: Given 40% of 5 employees including 1 who are capable of doing task.
40% of 5 employeees
= 40/100 * 5
= 2 employees
===> 1 employees who are capable of doing the task and one employee who is not capable.
percentage of employees assigned who are not capable
= 1/2 * 100
= 50%
ANSWER:C
Answer: C
Question: A man spends Rs. 1600 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 . 4000 a year. What is his average monthly income?
Options:
A)2000
B)2010
C)2100
D)2200
E)2300
Rationale: Total expenditure for the first 3 months = 3 × 1600 = 4800
Total expenditure for 4 months = 4 × 1550 = 6200
Total expenditure for 5 months = 5 × 1800 = 9000
Total expenditure and saving (which is income for one year)
= 4800 + 6200 + 9000 + 4000 = Rs. 24000
So, Average monthly income = 24000/12 = Rs. 2000
A
Answer: A
Question: At 1:00 PM, Train X departed from Station A on the road to Station B. At 1:10 PM, Train Y departed Station B on the same road for Station A. If Station A and Station B are p miles apart, Train X’s speed is r miles per hour, and Train Y’s speed is s miles per hour, how many hours after 1:00 PM, in terms of p, r, and s, do the two trains pass each other?
Options:
A)0.5 + (p - 0.5s)/(r + s)
B)(p - 0.5s)/(r + s)
C)0.5 + (p - 0.5r)/r
D)(p - 0.5r)/(r + s)
E)0.5 + (p - 0.5r)/(r + s)
Rationale: The distance A is going to cover between 1:00 and 1:30
= .5r
now the distance between the two trains = (p-.5r)
the relative velocity = (r-(-s)) = r+s
From 1:30, time is going to take when they meet = (p-.5r)/(r+s)
so the ans is .5+((p-.5r)/(r+s)) [.5 is added for the time from 1:00 to 1:30]
ans is A
Answer: A
Question: The average age of 17 students of a class is 17 years. Out of these, the average age of 5 students is 14 years and that of the other 9 students is 16 years, The age of the 17th student is
Options:
A)62
B)66
C)18
D)75
E)12
Rationale: Explanation:
Age of the 17th student = [17 * 17 - (14 * 5 + 16 * 9)] = (289-214) = 75 years.
Answer: D
Answer: D
Question: If the consumer price index for a sample of goods and services purchased in Dallas rose from 100 at the end of 1967 to x at the end of 1985, what was the average Y (arithmetic mean) annual increase in the index over this period?
Options:
A) (x + 100)/18
B) x/18
C) (100 − x)/18
D) (x − 100)/18
E) 100x/18
Rationale: CPI in end of 1967 = 100
CPI in end of 1985 = x
Number of years = 18
Average annual increase in CPI Y= (x-100)/18
Answer D
Answer: D
Question: If 1,000 microns = 1 decimeter, and 1,000,000 angstroms = 1 decimeter, how many angstroms equal 1 micron?
Options:
A)100
B)10
C)1,000
D)10,000
E)100,000
Rationale: Given that 1,000 microns = 1 decimeter =1,000,000 angstroms
So, 1 micron = 1,000,000/1,000
=1,000
Answer : C
Answer: C
Question: Kate and Danny each have $10. Together, they flip a fair coin 5 times. Every time the coin lands on heads, Kate gives Danny $1. Every time the coin lands on tails, Danny gives Kate $1. After the five coin flips, what is the probability M that Kate has more than $10 but less than $15?
Options:
A)5/16
B)1/2
C)M=12/30
D)M=15/32
E)M=3/8
Rationale: For 21 heads Kate will end up with < $10 and we want her to win. Therefore, only possibilities are 3 or 4 heads.
I made an educated guess and it worked fine.
Ans- 'D'
MGMAT's anagram helped here as well.
HHHHT = 5!/4!*1! = 5
HHHTT = 5!/3!*2! = 10
Total acceptable cases = 15
Total cases = 32
P = 15/32.D
Answer: D
Question: A cyclist traveled for two days. On the second day the cyclist traveled 4 hours longer and at an average speed 10 mile per hour slower than she traveled on the first day. If during the two days she traveled a total of 280 miles and spent a total of 10 hours traveling, what was her average speed on the second day?
Options:
A)5 mph
B)10 mph
C)20 mph
D)30 mph
E)40 mph
Rationale: SOLUTION:
D = 280 Mi
T = 12 hrs
Day 1 time = T1
Day 2 time = T2
T2 - T1 = 4 hrs ----- (I)
T1 + T2 = 12 hrs ----- (II)
Adding I and II, T2 = 8 hrs and T1 = 4 hrs
Day 1 Rate = R1
Day 2 Rate = R2
R1 - R2 = 10 mph
i.e. R1 = 10 + R2
280 = 8R2 + 4R1
i.e. 280 = 8R2 + 4 (10 + R2)
i.e. R2 = 20 mph
ANSWER: E
Answer: E
Question: If we listed all numbers from 100 to 10,000, how many times would the digit 3 be printed?
Options:
A)3980
B)3700
C)3840
D)3780
E)3680
Rationale: DETAILED SOLUTION
We need to consider all three digit and all 4-digit numbers.
Three-digit numbers: A B C. 3 can be printed in the 100’s place or 10’s place or units place.
=> 100’s place: 3 B C. B can take values 0 to 9, C can take values 0 to 9. So, 3 gets printed in the 100’s place 100 times
=> 10’s place: A 3 C. A can take values 1 to 9, C can take values 0 to 9. So, 3 gets printed in the 10’s place 90 times
=> Unit’s place: A B 3. A can take values 1 to 9, B can take values 0 to 9. So, 3 gets printed in the unit’s place 90 times
So, 3 gets printed 280 times in 3-digit numbers
Four-digit numbers: A B C D. 3 can be printed in the 1000’s place, 100’s place or 10’s place or units place.
=> 1000’s place: 3 B C D. B can take values 0 to 9, C can take values 0 to 9, D can take values 0 to 9. So, 3 gets printed in the 100’s place 1000 times.
=> 100’s place: A 3 C D. A can take values 1 to 9, C & D can take values 0 to 9. So, 3 gets printed in the 100’s place 900 times.
=> 10’s place: A B 3 D. A can take values 1 to 9, B & D can take values 0 to 9. So, 3 gets printed in the 10’s place 900 times.
=> Unit’s place: A B C 3. A can take values 1 to 9, B & C can take values 0 to 9. So, 3 gets printed in the unit’s place 900 times.
3 gets printed 3700 times in 4-digit numbers.
So, there are totally 3700 + 280 = 3980 numbers.
CORRECT ANSWER : A
Answer: A
Question: The price of rice falls by 20%. How much rice can be bought now with the money that was sufficient to buy 20 kg of rice previously?
Options:
A)5 kg
B)15 kg
C)25 kg
D)30 kg
E)None
Rationale: Solution: Let Rs. 100 be spend on rice initially for 20 kg.
As the price falls by 20%, new price for 20 kg rice,
= (100 -20% of 100) = 80
New price of rice = 80/20 = Rs. 4 per kg.
Rice can bought now at = 100/4 = 25 kg.
Answer: Option C
Answer: C
Question: In a group of cows and chickens, the number of legs was 14 more than twice the number of heads. The number of cows was:
Options:
A)5
B)7
C)10
D)12
E)14
Rationale: Let the number of cows be x and their legs be 4x.
Let the number of chicken be y and their legs be 2x.
Total number of legs = 4x + 2y.
Total number of heads = x + y.
The number of legs was 14 more than twice the number of heads.
Therefore, 2 × (x + y) + 14 = 4x + 2y.
or, 2x + 2y + 14 = 4x + 2y.
or, 2x + 14 = 4x [subtracting 2y from both sides].
or, 14 = 4x – 2x [subtracting 2x from both sides].
or, 14 = 2x.
or, x = 7 [dividing by 2 on both sides].
Therefore, the number of cows = 7.
Correct Answer:B)7
Answer: B
Question: If N = 1000x + 100y + 10z, where x, y, and z are different positive integers less than 4, the remainder when N is divided by 9 is
Options:
A)2
B)4
C)6
D)8
E)9
Rationale: Since we cannot have more than one correct answers in PS questions, then pick some numbers for x, y, and z and find the reminder when 1000x + 100y + 10z is divided by 9.
Say x=1, y=2, and z=3, then 1000x + 100y + 10z = 1,230 --> 1,230 divide by 9 yields the remainder of 6 (1,224 is divisible by 9 since the sum of its digit is a multiple of 9, thus 1,230, which is 6 more than a multiple of 9, yields the remainder of 6 when divided by 9).
Answer; C.
Answer: C
Question: Three times a number is 20% more than twice another number when increased by 105. If twice the first number increased by 36 is 20% less than three times of the second number, then what is the first number?
Options:
A)150
B)162
C)180
D)170
E)160
Rationale: Let the two numbers be x and y.
3x = 1.2( 2y +105)
3x = 2.4y +126 ………………..(1)
2x +36 = 0.8(3y)
2x +36 =2.4y ………………..(2)
x = 162
ANSWER:B
Answer: B
Question: Ram sold two bicycles, each for Rs.990. If he made 10% profit on the first and 10% loss on the second, what is the total cost of both bicycles?
Options:
A)2000
B)2879
C)2700
D)2797
E)2761
Rationale: (10*10)/100 = 1%loss
100 --- 99
? --- 1980 => Rs.2000
Answer:A
Answer: A
Question: A license plate in the country Kerrania consists of four digits followed by two letters. The letters A, B, and C are used only by government vehicles while the letters D through Z are used by non-government vehicles. Kerrania's intelligence agency has recently captured a message from the country Gonzalia indicating that an electronic transmitter has been installed in a Kerrania government vehicle with a license plate starting with 79. If it takes the police 14 minutes to inspect each vehicle, what is the probability that the police will find the transmitter within three hours?
Options:
A) 18/79
B) 1/6
C) 1/25
D) 1/50
E) 7/450
Rationale: Everything is correct except that you assumed the letters can't be repeated. It can be repeated.
AA
BB
CC
AB, AC, BC, BA, CA, CB.
Thus; total government vehicles = (10)^2*(3)^2 = 100*9 = 900
Vehicles inspected within 3 hours = 60*3/14 = 14
P = 14/900 = 7/450
Ans:E
Answer: E
Question: When a Mobile is sold for Rs. 24000, the owner loses 40%. At what price must that Mobile be sold in order to gain 40%?
Options:
A)54,000
B)56,000
C)58,000
D)60,000
E)62,000
Rationale: 60 : 24000 = 140 : x
x = (24000 x 140)/60 = 56000.
Hence, S.P. = Rs. 56,000.
Answer: Option B
Answer: B
Question: A can empty the tank in 28 hrs, B can fill the tank in 14 hrs, and C takes 7 hrs for filling.
If all three pipes are opened simultaneously ,how long it will take to fill the tank?
Options:
A)4 hr 36 minutes
B)5 hr 36 minutes
C)6 hr 36 minutes
D)7 hr 36 minutes
E)None of these
Rationale: Solution:time taken=(28*14*7*)/(28*14 - 14*7 + 28*7)
To solve this quicker find out LCM(28,14,7)
we get 28
Time taken =28/(-28/28 +28/14 + 28/7)
=28/(-1+2+4)
=28/5
=5.6 hrs
=5 hr 36 minutes
Answer B
Answer: B
Question: Vijay bought 160 shirts at the rate of Rs. 225 per shirt. The transport expenditure was Rs. 1400. He paid an octroi at the rate of Rs. 1.75 per shirt and labour charges were Rs. 320. What should be the selling price of one shirt, if he wants a profit of 60%?
Options:
A)282
B)229
C)277
D)380
E)2812
Rationale: Total CP per shirt = 225 + 1400/160 + 1.75 + 320/160 = Rs. 237.5
SP = CP[(100 + profit%)/100]
= 237.5 * [(100 + 60)/100] = Rs. 380.
Answer:D
Answer: D
Question: If a and b are mixed in 3:5 ration and b and c are mixed in 8:5 ration if the final mixture is 35 liters, find the amount of b?
Options:
A)13.73 ltrs
B)14.73 ltrs
C)15.73 ltrs
D)16.73 ltrs
E)17.73 ltrs
Rationale: Ratio of abc will be 24 :40:25,
Amt of b in 35 litr of mixture of a,b,c = 40*35/89 =15.73 ltrs
ANSWER:C
Answer: C
Question: The two trains of lengths 400 m, 600 m respectively, running at same directions. The faster train can cross the slower train in 180 sec, the speed of the slower train is 48 km. then find the speed of the faster train?
Options:
A)28
B)68
C)66
D)51
E)11
Rationale: Length of the two trains = 600m + 400m
Speed of the first train = X
Speed of the second train= 48 Kmph
1000/X - 48 = 180
1000/x - 48 * 5/18 = 180
50 = 9X - 120
X = 68 Kmph
Answer: B
Answer: B
Question: The simple interest and the true discount on a certain sum for a given time and at a given rate are Rs. 85 and Rs. 75 respectively. The sum is:
Options:
A)1360
B)637.5
C)1600
D)1800
E)None
Rationale: Sol.
Sum = S.I. * T.D. / (S.I)-(T.D.) = 85 * 75 / (85 - 75) = Rs.637.5.
Answer B
Answer: B
Question: Ramu bought an old car for Rs. 42000. He spent Rs. 8000 on repairs and sold it for Rs. 64900. What is his profit percent?
Options:
A)29.8%
B)16%
C)18%
D)82%
E)23%
Rationale: Total CP = Rs. 42000 + Rs. 8000 = Rs. 50000 and SP
= Rs. 64900
Profit(%) = (64900 - 50000)/50000 * 100
= 29.8%
Answer:A
Answer: A
Question: a certain organization has three committees. only two persons are members of all committees, but every pair of committees have three members in common. what is the least possible no of member of members on any one committee?
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: Total 4 members minimum required to serve only on one committee.
ANSWER:A
Answer: A
Question: A sum of money is borrowed and paid back in two annual installments of Rs. 882 each allowing 5% C.I. The sum borrowed was?
Options:
A)1277
B)1640
C)2877
D)1882
E)1811
Rationale: Explanation:
Principal = (P.W. of Rs. 882 due 1 year hence) + (P.W. of Rs. 882 due 2 years hence)
= [882/(1 + 5/100) + 882/(1 + 5/100)2]
= (882 * 20)/21 + (882 * 400)/441 = Rs. 1640.
Answer: B
Answer: B
Question: The present worth of a certain bill due sometime hence is Rs. 400 and the true discount is Rs. 20. What is the banker's discount?
Options:
A)Rs. 19
B)Rs. 22
C)Rs. 20
D)Rs. 21
E)None of these
Rationale: Explanation :
BG = (TD)2/PW=202/400= Rs. 1
BG = BD – TD
=> 1 = BD - 20
=> BD = 1 + 20 = Rs. 21 Answer : Option D
Answer: D
Question: There are 11 person among whom 2 are brother. The total no.of ways in which these persons can be seated around a round table so that exactly 1 person sit between the brothers, is equal to?
Options:
A)4!*2!
B)7!*2!
C)6!*1!
D)2!*1!
E)8!*2!
Rationale: Total number of ways = 8!*2!.
E
Answer: E
Question: In how many years will a sum of money doubles itself at 5% per annum on simple interest?
Options:
A)80%
B)20%
C)29%
D)30%
E)60%
Rationale: P = (P*5*R)/100
R = 20%
Answer: B
Answer: B
Question: Two trains 121 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet?
Options:
A)7.16
B)7.12
C)7.11
D)7.15
E)7.13
Rationale: T = (121 + 165)/ (80 + 65) * 18/5
T = 7.15
Answer: D
Answer: D
Question: From a total of 7 men and 3 women, how many ways to form a group of 5 men and 2 women ?
Options:
A)53
B)57
C)61
D)63
E)None of these
Rationale: Explanation :
Required number of ways = (7C5 3C2)
= (21*3)
= 63.
Answer : D
Answer: D
Question: Pipe A usually fills a tank in 2 hours. On account of a leak at the bottom of the tank, it takes pipe A 30 more minutes to fill the tank. How long will the leak take to empty a full tank if pipe A is shut?
Options:
A)7 hours
B)8 hours
C)9 hours
D)10 hours
E)11 hours
Rationale: Pipe A fills the tank normally in 2 hours. Therefore, it will fill ½ of the tank in an hour.
Let the leak take x hours to empty a full tank when pipe A is shut. Therefore, the leak will empty of the tank in an hour.
The net amount of water that gets filled in the tank in an hour when pipe A is open and when there is a leak = of the tank. — (1)
When there is a leak, the problem states that Pipe A takes two and a half hours to fill the tank. i.e. hours. Therefore, in an hour, of the tank gets filled. – (2)
Equating (1) and (2), we get => => x = 10 hours.
The problem can also be mentally done as follows.
Pipe A takes 2 hours to fill the tank. Therefore, it fills half the tank in an hour or 50% of the tank in an hour.
When there is a leak it takes 2 hours 30 minutes for the tank to fill. i.e hours to fill the tank or or 40% of the tank gets filled.
On account of the leak, (50 - 40)% = 10% of the water gets wasted every hour. Therefore, the leak will take 10 hours to drain a full tank.
ANSWER:D
Answer: D
Question: A telephone number contains 10 digit, including a 3-digit area code. Bob remembers the area code and the next 5 digits of the number. He also remembers that the remaining digits are not 1, 6, or 7. If Bob tries to find the number by guessing the remaining digits at random, the probability that he will be able to find the correct number in at most 2 attempts is closest to which of the following?
Options:
A)1/7
B)1/14
C)1/28
D)2/49
E)2/81
Rationale: There are 7*7 = 49 possibilities.
Bob has 2 chances so the probability is 2/49.
The answer is D.
Answer: D
Question: 5n + 7 > 12 and 7n - 5 < 44; n must be between which numbers?
Options:
A)1 and 8
B)2 and 6
C)0 and 9
D)1 and 7
E)2 and 9
Rationale: 5n > 5 --> n > 1
7n < 49 --> n < 7
1 < n < 7
Answer: D
Answer: D
Question: A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?
Options:
A)35 hrs
B)20 hrs
C)10 hrs
D)15 hrs
E)50 hrs
Rationale: Pipe A alone take x hrs
then pipe B and C will take x/2 and x/4 hrs
=>1/x+2/x+4/x=1/x=>7/x=1/5
x = 35 hrs
ANSWER A
Answer: A
Question: The weight of four dogs is determined to be 25 pounds, 31 pounds, 35 pounds and 33 pounds respectively. The weight of a fifth dog is determined to be y pounds. If the average (arithmetic mean) weight of the first four dogs is the same as that of all five dogs what is the value of y?
Options:
A)31
B)33
C)35
D)37
E)39
Rationale: Total weight of the 4 dogs = (25+31+35+33) = 124
Avg = 124/4 = 31
Total weight of 5 dogs = 124+y or 4(31)+y
Average of 5 dogs as per Question = 31
Equation:
4(31) + y = 5 (31), or y = 31.
Choose A
Answer: A
Question: The sum of three consecutive even numbers is 42. Find the middle number of the three?
Options:
A)5
B)8
C)96
D)32
E)14
Rationale: Explanation:
Three consecutive even numbers (2P - 2), 2P, (2P + 2).
(2P - 2) + 2P + (2P + 2) = 42
6P = 42 => P = 7.
The middle number is: 2P = 14.
Answer E
Answer: E