divelab/Sys2Bench huggingface dataset:
Question: Six cards numbered from 1 to 6 are placed in an empty bowl. First one card is drawn and then put back into the bowl; then a second card is drawn. If the cards are drawn at random and if the sum of the numbers on the cards is 8, what is the probability that one of the two cards drawn is numbered 4 ?
Options:
A)1/3
B)1/2
C)1/6
D)1/5
E)1/4
Rationale: (6,2) (2,6) (5,3) (3,5) (4,4) – only 5 possible scenarios for sum to be 8. One from this 5 has already happened.
From this five cases, only in one we have 4. So, the probability is 1 chances out of 5 that the one that occurred had 4: P=1/5.
Answer: D.
Answer: D
Question: A man has Rs.10350 in the form of Rs.50 notes and Rs.500 notes. The total number of notes are 54.Find the number of notes of Rs.50 denomination.
Options:
A)15
B)21
C)37
D)19
E)21
Rationale: Total Money = Rs. 10350.
Let 50 rupees note was X.
Then 500 rupees note = 54 - X
Now,
50*X + 500 * (54 - X) = 10350
50X + 27000 - 500X = 10350
- 450X = - 16650
X = 37.
No. of 50 rupees note = 37.
Answer: Option C
Answer: C
Question: On dividing 2272 as well as 875 by 3-digit number N, we get the same remainder. The sum of the digits of N is?
Options:
A)8
B)10
C)12
D)16
E)18
Rationale: Clearly, (2272 - 875) = 1397, is exactly divisible by N.
Now, 1397 = 11 x 127
The required 3-digit number is 127, the sum of whose digits is 10
Option B
Answer: B
Question: Sue's trail mix is 30% nuts and 70% dried fruit. Jane's trail mix is 60% nuts and 40% chocolate chips. If the combined mixture of Sue and Jane's trails mix contains 45% nuts, what percent of the combined mixture is dried fruit?
Options:
A)25%
B)30%
C)35%
D)40%
E)45%
Rationale: 45% is 15%-points above 30% and 15%-points below 60%.
So the ratio of Sue's mix to Jane's mix is 1:1.
1/2*70% = 35%
The answer is C.
Answer: C
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively . If they cross each other in 22 seconds, what is the ratio of their speeds?
Options:
A)1:1
B)3:1
C)2:3
D)3:2
E)3:4
Rationale: Let the speed of the trains be x and y respectively
length of train1 = 27x
length of train2 = 17y
Relative speed= x+ y
Time taken to cross each other = 22 s
= (27x + 17 y)/(x+y) = 22
= (27x + 17 y)/ = 22(x+y)
= 5x = 5y
=x/y = 5/5 = 1/1 i.e 1:1
Answer :A
Answer: A
Question: Aamir saves 32% of his monthly salary. If he spends Rs. 27200, then find his savings?
Options:
A)29998
B)77827
C)26772
D)12800
E)21212
Rationale: Let the monthly salary of Aamir be Rs. x.
68% of x = 27200
=> x = (27200 * 100)/68 = 40000
His savings = 32/100 * 40000 = 12800.
Answer: D
Answer: D
Question: If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 3 years the amount to be paid is?
Options:
A)8118
B)8127
C)8618
D)8436
E)8128
Rationale: A = 7500(26/25)3
= 8436
Answer: D
Answer: D
Question: Jacob is now 12 years younger than Michael. If 5 years from now Michael will be twice as old as Jacob, how old will Jacob be in 4 years?
Options:
A) 3
B) 7
C) 11
D) 21
E) 25
Rationale: Jacob=x years, Mike=x+12 years
5 years from now,
2(x+5)=x+17
2x+10=x+17
x=7
x+4=11 years
Answer C
Answer: C
Question: Three numbers are in the ratio 4:2:5 and their H.C.F is 12. The numbers are:
Options:
A)4, 2, 5
B)5, 10, 15
C)10, 20, 30
D)48, 24, 60.
E)12, 24, 60
Rationale: Let the required numbers be 4x, 2x and 5x. Then, their H.C.F = x. So, x = 12.
The numbers are 48, 24, 60.
ANSWER:D
Answer: D
Question: Pencils, Pens and Exercise books in a shop are in the ratio of 14: 4 : 3. If there are 140 pencils, the number of exercise books in the shop is:
Options:
A)30
B)27
C)35
D)33
E)37
Rationale: Explanation :
Let Pencils = 14x, Pens = 4x & Exercise books = 3x.
Now, 14x = 140
hence x = 10
Number of exercise books = 3x = 30
Answer : A
Answer: A
Question: A money lender lends Rs.2000 for six months at 20% p.a. rate. It the interest is reckoned quarterly than find the amount given after time limit?
Options:
A)2205
B)1978
C)2834
D)2827
E)2781
Rationale: A = 2000(21/20)2
= 2205
Answer: A
Answer: A
Question: The average weight of a group of boys is 30 kg. After a boy of weight 35 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ?
Options:
A)4
B)8
C)9
D)2
E)9
Rationale: Let the number off boys in the group originally be x.
Total weight of the boys = 30x
After the boy weighing 35 kg joins the group, total weight of boys = 30x + 35
So 30x + 35 + 31(x + 1) = > x = 4.
Answer:A
Answer: A
Question: The last time Meena bought Diwali cards, he found that the three types of cards that he liked were priced Rs.2.00, Rs.3.50, Rs.4.50 each. As Meena wanted 30 cards, she took ten each of three cards , putting down the exact number of 10 rupees notes on the counter payment. How many notes did Meena give?
Options:
A)5
B)15
C)10
D)12
E)13
Rationale: Explanation :
Let the three cards be a, b ,c . 'x' be the number of notes.
Then, according to the question,
=> 10a + 10b + 10c = 10*x.
=> a + b + c= x . -----------------------------(i)
Since, a + b +c= 3.5 + 4.5 +2.0= x
x =10
Answer : C
Answer: C
Question: A train traveling at 72 kmph crosses a platform in 30 seconds and a man standing on the platform in 15 seconds. What is the length of the platform in meters?
Options:
A)240 meters
B)360 meters
C)300 meters
D)600 meters
E)Cannot be determined
Rationale: Speed of the train in metres/sec = 72000/3600 = 20
Distance travelled by train to cross the platform = 30 * 20 = 600 = Length of train + Length of platform
Distance travelled by train to cross the man = 15 * 20 = 300 = Length of train
Length of platform = 600 - 300 = 300
Answer: C
Answer: C
Question: A jar is filled with red, white, and blue tokens that are equivalent except for their color. The chance of randomly selecting a red token, replacing it, then randomly selecting a white token is the same as the chance of randomly selecting a blue token. If the number of tokens of every color is a multiple of 2, what is the smallest possible total number of tokens in the jar?
Options:
A) 9
B) 12
C) 15
D) 18
E) 21
Rationale: (Red / Total Coins)*(White / Total Coins) = (Blue / Total Coins)
i.e. Red*White = Blue*Total Coins
Let, Red = 3a
White = 3b
Blue = 3c
Total Coins = 3(a+b+c)
i.e. 3a * 3b = 3c*3(a+b+c)
i.e. a*b = c*(a+b+c)
For smallest values of a, b and c
2*3 = 1*(1+2+3)
i.e. Minimum Total Coins = 3*(1+2+3) = 18
Answer: Option B
Answer: B
Question: Lottery balls numbered consecutively from one through one hundred are placed in a spinner. If one ball is drawn at random, what is the probability that it will have the number 5 on it exactly once?
Options:
A)9/100
B)1/10
C)18/100
D)19/100
E)1/5
Rationale: Probability = No of balls with exactly one 1 / total number of balls
= {5,15,25,35,45,50,51,52,53,54,56 to 59,65,75,85,95}/100
= 18/100
Answer is C
Answer: C
Question: Which of the following is the equation of the line in the xy-plane that has slope 0
(I) x = 2
(II) y = 6
(III) x + y = 0
Options:
A)II &III
B)III
C)I and II only
D)I
E)II
Rationale: y =mx+c therefore y-c= mx then m =(y-c)/x
m=0 means y = c constant ..= II
E
Answer: E
Question: Ravi and Kavi start a business by investing ₹ 8000 and ₹ 72000, respectively. Find the ratio of their profits at the end of year.
Options:
A)2 : 9
B)5 : 9
C)7 : 9
D)1 : 9
E)3 : 9
Rationale: Ratio of profit = Ratio of investments
= 8000 : 72000 = 1 : 9
Answer : D
Answer: D
Question: 33 1/3% OF 360?
Options:
A)80
B)90
C)110
D)120
E)130
Rationale: 33 1/3 % = 1/3
1/3 × 360 = 120
D)
Answer: D
Question: Find the average of first 97 natural numbers.
Options:
A)47
B)37
C)48
D)49
E)49.5
Rationale: Solution: 1st Method:
Average of 1st n natural number is given by = ([n*(n+1)]/2)/n
Average of 1st 97 natural number is given by = {([97*(97+1)]/2)/97} = 49
2nd Method:
These numbers are in AP series, so average,
= (sum of corresponding term)/2
= (1+97)/2 = 49
Or, (2+96)/2 = 49
Or, (3+95)/2 = 49 And so on.
Answer: Option D
Answer: D
Question: Here 10 programmers, type 10 lines within 10 minutes then 60 lines can type within 60 minutes. How many programmers are needed?
Options:
A)16
B)10
C)6
D)60
E)50
Rationale: 10
10 programmer 10 line 10 mins.
10 programmer 20 line 20 mins.
.
.
.
.10 programmer 60 line 60 mins.
ANSWER:D
Answer: D
Question: A dog takes 3 leaps for every 8 leaps of a hare. If one leap of the dog is equal to 3 leaps of the hare, the ratio of the speed of the dog to that of the hare is :
Options:
A)9:8
B)9:9
C)9:6
D)9:1
E)9:2
Rationale: Explanation:
Dog : Hare = (3*3) leaps of hare : 8 leaps of hare = 9 : 5.
Answer: A) 9:8
Answer: A
Question: If rupee one produces rupees nine over a period of 54 years, find the rate of simple interest?
Options:
A)22 1/7 %
B)22 3/2 %
C)22 1/8 %
D)22 1/2 %
E)16 2/3 %
Rationale: 9 = (1*54*R)/100
R = 16 2/3 %
Answer:E
Answer: E
Question: A soft drink company had 5000 small and 12000 big bottles in storage. If 15% of small 18% of big bottles have been sold, then the total bottles remaining in storage is
Options:
A)14090
B)16010
C)15060
D)14930
E)16075
Rationale: 5000 + 12000 - (0.15*5000 + 0.18*12000) = 14090.
Answer: A.
Answer: A
Question: A housewife saved Rs. 2.50 in buying an item on sale. If she spent Rs. 25 for the item, approximately how much percent she saved in the transaction ?
Options:
A)9%
B)10%
C)7%
D)6%
E)None of these
Rationale: Explanation :
Actual Price = Rs.25 + Rs.2.50 = Rs.27.5
Saving = Rs.2.5
Percentage Saving = (2.5/27.5) × 100 = 250/27.5 = 2500/275
= 100/11 = 9(1/11)% ≈ 9%
Answer : Option A
Answer: A
Question: The sum of five consecutive even numbers of set x is 440. Find the sum of a different set of five consecutive integers whose second least number is 121 less than double the least number of set x?
Options:
A)776
B)240
C)872
D)2667
E)712
Rationale: Let the five consecutive even numbers be 2(x - 2), 2(x - 1), 2x, 2(x + 1) and 2(x + 2)
Their sum = 10x = 440
x = 44 => 2(x - 2) = 84
Second least number of the other set = 2(84) - 121 = 47
This set has its least number as 46.
Sum of the numbers of this set = 46 + 47 + 48 + 49 + 50
= 48 - 2 + 48 - 1 + 48 + 48 + 1 + 48 + 2 => 5(48) = 240
Answer: B
Answer: B
Question: The weights of one liter vegetable ghee packet of two brands ‘A’ and ‘B’ are 950 gm and 850 gm respectively. If they are mixed in the ratio of 3 : 2 by volumes to form a mixture of 4 liters, what is the weight (in kg) of the mixture?
Options:
A)3.64
B)1.75
C)3.52
D)2.72
E)None of these
Rationale: Here's how I did it. My notes from reading the problem were:
1L A = 950 gm
1L B = 850 gm
We are mixing five parts (3 parts A plus 2 parts B, 5 parts total) to get 4L, so 5x = 4 ---> x = 4/5. Each part is 4/5 of a liter.
So if we have 3 parts A, we have 950*3*(4/5) = 2280
If we have 2 parts B, we have 850*2*(4/5) = 1360
2280 + 1360 = 3640
Solving for units gives us 3.64
So the answer is A
Answer: A
Question: Judges will select 4 finalists from the 7 contestants entered in a singing competition. The judges will then rank the contestants and award prizes to the 3 highest ranked contestants: a blue ribbon for first place, a red ribbon for second place, and a yellow ribbon for third place. How many different arrangements of prize-winners are possible?
Options:
A)140
B)21
C)210
D)420
E)1,260
Rationale: First Select 4 from 7 contestants and then select top 3 from those 5 =
7C4*4C3 =35 * 4 = 140
ANS:A
Answer: A
Question: A circle is circumscribed around a quadrilateral, and the quadrilateral is ABCD, What is the value of arc ADC when angle D is 155 degrees?
Options:
A)125
B)100
C)75
D)50
E)25
Rationale: An inscribed angle is an angle in a circle composed of two chords with a common endpoint, that is, an angle with its vertex on the circle. In this problem, all four lettered angles are inscribed angles.
An inscribed angle necessarily opens to intersect an arc (the technical word is to subtend an arc). The Inscribed Angle Theorem said that the measure of an inscribed angle is always half the measure of the arc it intersects, or subtends.
angle D = 155 degrees
Thus,
arc ABC = 310 degrees
A whole circle has 360 degrees of arc, so arc ADC should be the rest of the circle.
arc ADC = 360 - 310 = 50 degrees
Answer =(D)
Answer: D
Question: what are the number of solutions for x+y+z=12, if x,y & z can take values from 1 to 7 ?
Options:
A)34
B)35
C)36
D)37
E)38
Rationale: if x=1, (y,z) can be (4,7)(5,6)(6,5)(7,4)
if x=2, (y,z) can be (3,7)(4,6)(5,5)(6,4)(7,3)
if x=3, (y,z) can be (2,7)(3,6)(4,5)(5,4)(6,3)(7,2)
if x=4, (y,z) can be (1,7)(2,6)(3,5)(4,4)(5,3)(6,2)(7,1)
if x=5, (y,z) can be (1,6)(2,5)(3,4)(4,3)(5,2)(6,1)
if x=6, (y,z) can be (1,5)(2,4)(3,3)(4,2)(5,1)
if x=7, (y,z) can be (1,4)(2,3)(3,2)(4,1)
Total Combination = 4+5+6+7+6+5+4=37
ANSWER:D
Answer: D
Question: An error 5% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is
Options:
A)10.4%
B)10.25%
C)10.23%
D)10.26%
E)10.5%
Rationale: 100 cm is read as 102 cm.
A1 = (100 x 100) cm2 and A2 (105 x 105) cm2.
(A2 - A1) = [(105)2 - (100)2]
= (105 + 100) x (105 - 100)
= 1025 cm2.
Percentage error = 10.25
B
Answer: B
Question: A pupil's marks were wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by half (1/2). The number of pupils in the class is:
Options:
A)10
B)20
C)30
D)40
E)50
Rationale: x pupils in class
total increase = (x*1/2) = x/2
x/2=(83-63) = 20 x= 40
ANSWER D
Answer: D
Question: Train A and Train B began traveling towards each other from opposite ends of a 500-mile long track at 1:00 PM. If Train A traveled at 25 miles per hour and Train B traveled at 25 miles per hour, at what time did the trains meet?
Options:
A)5:40 PM
B)11:00 PM
C)7:20 PM
D)8:00 PM
E)9:20 PM
Rationale: This question tests your concepts of relative speed:
If two trains are moving in opposite direction, then distance will reduce at a rate of (Speed of 1 + Speed of 2)
If two trains are moving in same direction, then distance will reduce at a rate of (Speed of 1 - Speed of 2)
Here the trains are moving towards each other, hence in opposite direction.
Trains will cover the 500 mile track in a time of 500/(25 + 25) = 500/50 = 10 hours
Trains started at 1:00 PM, there they will meet at 11:00 PM
Option B
Answer: B
Question: A bag contains 13 wool scarves, exactly one of which is red and exactly one of which is green. If Deborah reaches in and draws three scarves, simultaneously and at random, what is the probability that she selects the red scarf but not the green scarf?
Options:
A)3/16
B)4/23
C)5/26
D)7/34
E)9/47
Rationale: Total possible ways to choose three scarves is 13C3 = 286
We need to choose the red scarf and two of 11 other scarves (not the green scarf).
The number of successful possibilities is 11C2 = 55
P(red scarf but not green scarf) = 55/286 = 5/26
The answer is C.
Answer: C
Question: The speed of a boat in still water is 36 kmph. What is the speed of the stream if the boat can cover 80 km downstream or 40 km upstream in the same time?
Options:
A)10 kmph
B)14 kmph
C)12 kmph
D)16 kmph
E)15 kmph
Rationale: X = the speed of the stream
(36 + X) / (36 - X) = 2/1
36+ X = 72 - 2X
3X = 36
X = 12 km/hour
If the speed of the stream is 12km/hour, then the 'downstream' speed of the boat is 36+12= 48km/hour and the 'upstream' speed of the boat is 36-12 = 24km/hour. In that way, if the boat traveled for 2 hours, it would travel 2x48 = 96km downstream and 2x24 = 48 km/hour upstream.
Answer : C
Answer: C
Question: Find the largest 4 digit number which isexactly divisible by 88?
Options:
A)2413
B)4356
C)9944
D)7939
E)4674
Rationale: Largest 4 digit number is 9999
After doing 9999 ÷ 88 we get remainder 55
Hence largest 4 digit number exactly divisible by 88 = 9999 - 55 = 9944
C
Answer: C
Question: Working together, A and B can do a job in 6 days. B and C can do the same job in 10 days, while C and A can do it in 7.5 days. How long will it take if all A, B and C work together to complete the job?
Options:
A)4 days
B)5 days
C)8 days
D)9 days
E)10 days
Rationale: A and B 1day work = 1/6
B and C 1day work = 1/10
c and A 1day work =1/7.5
A,B,C 1day work =(1/6 + 1/10 + 1/7.5)*1/2=1/5
so A.B.C completes work in 5 days
ANSWER:B
Answer: B
Question: A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 24 hrs and a machine of type S does the same job in 12 hours. If the company used the same number of each type of machine to do the job in 4 hours, how many machines of type R were used?
Options:
A)2
B)4
C)6
D)9
E)12
Rationale: Rate of machine R = 1/24
Rate of machine S = 1/12
Rate of R+S = 1/8
To finish the work in 4 hrs, the combined rate needs to be 1/4.
x * 1/8 = 1/4
x = 2
The answer is A.
Answer: A
Question: A 160 meter long train crosses a man standing on the platform in 16 sec. What is the speed of the train?
Options:
A)36 kmph
B)54 kmph
C)92 kmph
D)86 kmph
E)76 kmph
Rationale: S = 160/16 * 18/5 = 36 kmph
ANSWER:A
Answer: A
Question: There are 32 people in a party. If everyone is to shake hands with one another, how many hand shakes are possible?
Options:
A)496
B)367
C)361
D)297
E)261
Rationale: Explanation:
Total number of persons = n = 32
Shake hands involve only 2 persons = r = 2
Number of shake hands = nCr = 32C2
32C2 = (32 * 31) /(2 * 1) = 496
ANSWER:A
Answer: A
Question: 40% of the population of a village is 23040. The total population of the village is ?
Options:
A)57600
B)44000
C)34936
D)25640
E)None
Rationale: Answer
∵ 40% of P = 23040
∴ P = (23040 x 100) / 40 = 57600
Correct Option: A
Answer: A
Question: One side of a rectangular field is 15 m and one of its diagonals is 17 m. Find the area of the field.
Options:
A)111 m^2
B)120 m^2
C)130 m^2
D)124 m^2
E)131 m^2
Rationale: Other side = ((17) 2- (15)2)(1/2) = (289- 225)(1/2) = (64)(1/2) = 8 m.
Area = (15 x 8) m2 = 120 m2.
ANSWER B 120 m^2
Answer: B
Question: Three friends are buying a gift for a friend. Declan contributes 3 dollars more than 1/4 the cost of the gift, Ed contributes 1 dollar less than 1/3 the cost of the gift, and Frank contributes the remaining 22 dollars. What is the cost of the gift?
Options:
A)48
B)57.6
C)60
D)66
E)72
Rationale: Declan = D, Ed = E, Frank = F
t = total
D + E + F = t
(t/4 + 3) + (t/3 - 1) + 22 = t
t = 24 + (7t/12)
12t = 24(12) + 7t
5t = 24(12)
t = 57.6
The correct answer is B.
Answer: B
Question: The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).
Options:
A)8, 20, 28
B)16, 28, 36
C)16, 28, 35
D)16, 28, 34
E)16, 28, 33
Rationale: Let their present ages be 4x, 7x and 9x years respectively.
Then, (4x - 8) + (7x - 8) + (9x - 8) = 56
20x = 80
x = 4.
Their present ages are 4x = 16 years, 7x = 28 years and 9x = 36 years respectively.
Answer:B
Answer: B
Question: Find the value of 658217 x 99999 = m?
Options:
A)65842158943
B)65839570421
C)65821141683
D)66821785904
E)65821041783
Rationale: 658217 x 99999 = 658217 x (100000 - 1)
= 658217 x 100000 - 658217 x 1
= 65821700000 - 658217
= 65821041783
E
Answer: E
Question: The largest 4 digit number exactly divisible by 88 is?
Options:
A)9930
B)9936
C)9944
D)9952
E)9960
Rationale: Largest 4-digit number = 9999
88) 9999 (113
88
----
119
88
----
319
264
---
55
---
Required number = (9999 - 55)
= 9944.
C)
Answer: C
Question: A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of A?
Options:
A)3002
B)3000
C)3018
D)3019
E)3012
Rationale: 60*5:36*6:75*3
100: 72: 75
100/247 * 7410 = 3000
Answer: B
Answer: B
Question: Four men and three women can do a job in 6 days. When five men and six women work on the same job, the work gets completed in 4 days. How long will a woman take to do the job, if she works alone on it?
Options:
A)54 days
B)53 days
C)52 days
D)44 days
E)50 days
Rationale: 24m+18w=20m+24w
=>1m=3/2w
3(1/3w)+3w=1/6=
>w=54 days
ANSWER:A
Answer: A
Question: Given 2 negative numbers, the lesser is 5 less than twice the greater number. What is the greater number if the product of both numbers is 228?
Options:
A)-11
B)-14
C)-12
D)-18
E)-11
Rationale: Test the options. The options give you the greater number. Start from the middle option.
(C) - 12
Twice of -12 is -24 and 5 less is -19.
-19 * -12 = 228 (Correct)
Answer (C)
Answer: C
Question: The tax on a commodity is diminished by 10% and its consumption increases by 10%. Find the effects on revenue ?
Options:
A)1% decrease
B)2% increase
C)3% decrease
D)4% decrease
E)none of these
Rationale: Since tax consumption = revenue .
Therefore, Net % change in revenue
= ( x + y + xy/100) %
= [ - 10 + 10 + ( - 10 x 10)/100]% or -1% .
Therefore, revenue decreased by 1%.
ANSWER:A
Answer: A
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. 33820. What percentage of profit did he make?
Options:
A)80%
B)49%
C)40%
D)52%
E)90%
Rationale: The total CP = Rs. 16000 + Rs. 6250
= Rs. 22250 and SP = Rs. 33820
Profit(%) = (33820 - 22250)/22250 * 100
= 52%
Answer:D
Answer: D
Question: If 0.75 : x :: 5 : 8, then x is equal to:
Options:
A)1.34
B)1.43
C)1.2
D)1.45
E)1.56
Rationale: C
1.20
(x x 5) = (0.75 x 8) x = 6/5 = 1.20
Answer: C
Question: The average age of three boys is 40 years and their ages are in proportion 8:10:22. What is the age in years of the youngest boy?
Options:
A)8
B)9
C)7
D)6
E)5
Rationale: 8x + 10x + 22x = 40
x =1
8x = 8
Answer:A
Answer: A
Question: From 5 positive numbers and 5 negative numbers, how many groups of 4 numbers, yielding a positive product, can be formed?
Options:
A)720
B)110
C)30
D)960
E)255
Rationale: The number of ways to choose 4 positive numbers is 5C4 = 5.
The number of ways to choose 4 negative numbers is 5C4 = 5.
The number of ways to choose 2 positive and 2 negative is 5C2*5C2 = 10*10 = 100.
The total number of groups is 5+5+100 = 110.
The answer is B.
Answer: B
Question: X and Y are both integers. If X/Y = 59.60, then what is the sum of all the possible two digit remainders of X/Y?
Options:
A)560
B)315
C)672
D)900
E)1024
Rationale: Remainder = 0.60 --> 60/100 --> Can be written as (60/4) / (100/4) = 15/25
So remainders can be 15, 30, 45, 60, ..... 90.
We need the sum of only 2 digit remainders --> 15 + 30 + 45 + 60 + 75 + 90 = 315
Answer: B
Answer: B
Question: Which of the following numbers is the biggest => [-1/7 , -7/8 , -9/10 , -12/13 , -34/35]
Options:
A)A)-1/7
B)B)-7/8
C)C)-9/10
D)D)-12/13
E)E)-34/35
Rationale: If we observe all the fractions just differ by one i.e denominator vs numerate.. in such case the biggest will be with large values... here all values are with -ve value...the least value is biggest. i.e. -1/7..
Hence A is correct answer...
Answer: A
Question: If a two-digit positive integer has its digits reversed, the resulting integer differs from the original by 54. By how much do the two digits differ?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: Let’s first label the original two-digit integer as N. We can then say that N = 10A + B, where A is the tens digit and B is the units digit of N.
If this is hard to see let’s try it with a sample number, say 24. We can say the following:
24 = (2 x 10) + 4
24 = 20 + 4
24 = 24
Getting back to the problem, we are given that if the integer N has its digits reversed the resulting integer differs from the original by 54. First let’s express the reversed number in a similar fashion to the way in which we expressed the original integer.
10B + A = reversed integer
Since we know the resulting integer differs from the original by 54 we can say:
10B + A – (10A + B) = 54
10B + A – 10A – B = 54
9B – 9A = 54
B – A = 6
Since B is the tens digit and A is the units digit, we can say that the digits differ by 6.
The answer is D.
Answer: D
Question: In how many ways can four members be selected from a group of eight members?
Options:
A)10C6
B)10C8
C)8C4
D)8C3
E)10C1
Rationale: Four members can be selected from eight members in
10C6
= 8C4 ways.
Answer: C
Answer: C