IBA 58 Intake (Full solution )
If x is decreased from 2 to -2 , which of the following must increase ?
A) 2+x B. 5-x^2 C) 1+(1/x) D) 1/(x-3)
Answer :
A) 2+2=4 ; 2-2=0
So, it is decreased
5-2^2=1 ; 5-(-2)^2=1
Remain same
C) 1+(1/2)=3/2 ; 1-(1/2)=(1/2)
It is decreased
D) 1/(2-3)=-1 ; 1/(-2-3)=1/(-5)
It is increased
So Answer : D
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In a class of 25 students, 10 have less than 6 marbles, 10 have more than 7 marbles, 4 have more than 8 marbles.How many students have more than 5 marbles but less than 9 marbles?
A) 10 B. 11 C) 12 D) 13 E) None
Answer :
10 students have < 6 marbles
# 10 students have > 7 marbles
4 students have > 8 marbles
# 1 students have < 9 marbles
So 10+1 that is 11 (Ans.)
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A jogger running at 9 kmph alongside a railway track is 240 metres ahead of the engine of a 120 metres long train running at 45 kmph in the same direction.In how much time will the train pass the jogger ?
A) 3.6 sec B. 18 sec C) 36 sec D) 72 sec E) None
Answer :
MT=Initial separation/
Initial separation =240+120 that is 360 m
Relative speed =(45-9) kmph
=36*(5/18) that is 10 m/s
MT=360/10 that is 36 sec (Ans.)
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Arif sold 100 pens, of which 50 are red and 50 are black, at TK. 48 per pen.He made a profit of 20% on the black pens and made a loss of 20% on the red pens.what was the net gain on this sale ?
A) 0 B. -50 C) -100 D) -200 E) None
Answer :
Total SP=100*48 that is 4800
SP of red pen=50*48=2400
SP of black pen=50*48=2400
Total CP=2400*(5/
So Loss=200 (Ans.)
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7 years ago, Samir was 3 times as old as Saurov.In 4 years Samir will be twice as old as Saurov.What is Saurov’s present age?
A) 40 B. 18 C) 30 D) 20 E) None
Answer:
Approach-1:
Samir:Saurov =3:1 (7 yrs back)
Samir: Saurov =2:1 (After 4 yrs from present)
Age gap=7+4 that is 11
Samir age ratio gap=3-2 that is 1
ATQ 1==11
So 1 is also 11.
Saurov ‘s present age=11+7 that is 18 (Ans.)
Approach-2:
Saurov ‘s present age=S+7
Samir’s present age=3S+7
After 4 yrs:
3S+11=2(S+11)
=>S=11
So, Saurov ‘s age=S+7=11+7 that is 18 (Ans.)
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Box1 contains 500 marbles, 24% of which are black.Box2 contains some marbles of which 10% are black.You put the marbles together in another box and found that the percentage of black marbles is 20%.How many marbles were there in Box2?
A) 100 B. 150 C) 200 D) 250 E) None
Answer:
Approach-1:
Applying RoA :
24•••••••••••••
••••••••••••••2
=>10:4
=>5:2
ATQ 5==500
2==500*2/5 that is 200 (Ans.)
Approach-2:
24% of 500=120 are black
500-120 =380 are white
120+10% of x =20% of (500+x)
On solving, x=200 (Ans.)
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If -8<=x<=2 and -4<=y<=10 which of the following represents the range of all possible values of XY ?
Answer:
Possible values of XY are
1. (-8)*(-4)=32
2. 2*10=20
3. (-8)*10=-80
4. (-4)*2=-8
So, range is -80<=XY<=32 (Ans.)
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Raju has x number of books, which is 3 times as many as Siam and 1/2 As many as Payel.How many books do the three of them have altogether, in terms of x ?
A) 5x/6 B. 7x/3 C) 10x/3 D) 7x/2 E) None
Answer :
Raju has=x books
ATQ x=3*Siam
So Siam=(x/3) books
x==(1/2) of Piyal
So, Piyal =2x books
Cumulatively x+2x+(x/3) that is 10x/3 (Ans.)
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If y is an integer and 15<y<25, which of the following could be the average of 12,14,17,23 and y ?
A) 13.2 B. 15.6 C) 16.8 D) 18.2 E) 19.5
Answer :
Average value always lies in the middle.So, middle value is 17 which is near to 16.8 (Ans.)
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When a positive integer x is divided by 5 the remainder is 1. When x is divided by 8, the remainder is 4.What is the smallest positive integer y , such that (x+y) is divisible by 40?
A) 3 B.4 C) 9 D) 13 E) None
Answer :
If x=36 is taken thn all the conditions are satisfied.So, if x=36 then y must be 4 in order to divisible 36+4=40 by 40. So, y=4 (Ans.)
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At a certain bookstore,the regular price of each book is 20% less than it’s listed price.If during a sale, the price of each book at the store was 15% less than its regular price.The price of a book during the sale was what percent less than its listed price ?
A) 30% B) 32% C) 35% D) 38% E) None
Answer:
Approach-1:
LP:RP=5:4
RP:SP=20:17
LP:RP:SP=(5*20)
So 100-68 that is 32% less (Ans.)
Approach-2:
RP:LP=4:5
=80:100
During sale,
RP =80*(17/20) that is 68
So, LP=100
RP=68
So RP=32% less (Ans.)
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Silver is 26 times as heavy as Gold and Iron is 17 times as heavy as Gold.You have to prepare a mixture which is 23 times as heavy as Gold.what will be the ratio of Iron to silver in the mixture ?
A) 2:1 B. 2:3 C) 3:5 D) 1:2 E) None
Answer :
Applying RoA :
26•••••••••••••
••••••••••••23•
=>6:3
=>2:1 (Ans.)
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One year ago, the ratio of salary of Nasir and Gaurav was 5:8.Ratio between this year’s and last year’s salary of Nasir is 28:25 and the same for Gaurav’s is 23:20.If the sum of their present salary is TK. 1184, the difference between their present salary is :
A) TK. 448 B. TK. 340 C) TK. 288 D) TK.240 E) None
Answer :
Approach-1:
1 year Ago :
Ratio of N:G=5:8
=50:80
ATQ 25==50
28==50*28/25 that is 56
20==80
23==80*23/20 that is 92
Ratio of present salary:
N:G=56:92 or 14:23
ATQ 37==1184
9==1184*9/37 that is 288 (Ans.)
Approach-2:
25==5
28==5*28/25 that is 28/5 means 560%
Again 20==8
23==8*23/20 that is 46/5 means 920%
ATQ 1480%==1184
360%==1184*360/
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If x is an integer such that 5<x<11, 7<x<13 and x+2<12 then how many integers will satisfy x ?
A) 1 B. 2 C) 3 D) 4 E) None
Answer:
5<x<11
Here, 6,7,8,9,10 can be the value of x.
Again, 7<x<13
Here, 8,9,10,11,12 can be the value of x
Now, 8,9,10 are matched with both the conditions.
So, 8+2<12 ; 10<12 true
9+2<12 ; 11<12 true
10+2<12 ; 12<12 false
So there are two possible values of x (Ans.)
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John appointed 25 persons to complete a small bridge in 40 days. After 20 days, he appointed 15 more workers and the bridge was completed 5 days earlier.If he had not appointed additional workers by how many days he would have been behind the scheduled time ?
A) 2 B. 3 C) 4 D) 5 E) 7
Answer:
Applying MDH method :
25*40=25*20+40*
=>D=-4 days means 4 days behind the schedule (Ans.)
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At a certain club, the number of male members is twice that if female members.If 1/4 of male members are engineers and 1/5 of the female members are engineers, what fraction of the members are non-engineers ?
A) 13/25 B. 23/30 C) 2/5 D) 8/19 E) None
Answer: is attached in the comment box.
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Arif starts from A at 10 am towards B at 100 kmph.Babu starts from A at 10:10 am towards B at 120 kmph.Babu reached B 10 minutes before Arif.Calculate the distance between A and B
A) 100 B. 200 C) 240 D) 300 E) None
Answer:
Approach-1:
A:B=100:120 (Speed)
A:B=120:100 (Time)
ATQ 20==20
100==20*100/20 that is 100 minutes or 100/60 hr.
So D=120*(100/60) that is 200 km (Ans.)
Approach-2:
100*t=120(t-(1/
=>100t=120t-40
=>t=2 hr
So D=100*2 that is 200 km (Ans.)
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If ab<0 then all the following must be true EXCEPT
A) a/b<0 B. a^2+b^2>0 C) a^3+b^3<0 D) b/a<0 E) None
Answer :
We know that square always gives a positive value and cube always gives negative signs for the negative value.
So C is wrong due to its cube (Ans.)
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The cost of 12 pencils and 10 pens is 320.the cost of 20 pencils and 15 pens is 500.what is the difference between the cost of a pen and a pencil ?
A) 5 B. 10 C) 15 D) 20 E) None
Answer :
10 pen+12 pencil=320
=>2(5 pen+6 pencil)=320
=>5 pen+6 pencil=160•••(1
15 pen+20 pencil=500
=>5(3 pen+4 pencil)=500
=>3 pen+4 pencil=100•••(2
(1)*3-(2)*5 =>
15 pen+18 pencil=480
15 pen+20 pencil=500
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2 pencil=20
So, pencil =10
Pen=20
So, difference =20-10 that is 10 (Ans.)
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If x is an integer and y=-4x+17 what is the least value of x for which y is less than 1 ?
A) 2 B. 3 C) 4 D) 5 E) None
Answer:
If x=5 then y is less than 1
Ans. D
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Arif bought a pen at a 30% discount on listed price.Few months later , he found that the price for the same pen has increased by 50% and the discount he got in taka remained the same .How much discount did Arif get in terms of the new listed price ??
A) 10% B. 15% C) 20% D) 22.5% E) None
Answer :
LP=100
CP=70
Again LP=150
CP=150-30 that is 120
So, discount =(30/150)*100 that is 20% (Ans.)
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A) 2+x B. 5-x^2 C) 1+(1/x) D) 1/(x-3)
Answer :
A) 2+2=4 ; 2-2=0
So, it is decreased
5-2^2=1 ; 5-(-2)^2=1
Remain same
C) 1+(1/2)=3/2 ; 1-(1/2)=(1/2)
It is decreased
D) 1/(2-3)=-1 ; 1/(-2-3)=1/(-5)
It is increased
So Answer : D
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In a class of 25 students, 10 have less than 6 marbles, 10 have more than 7 marbles, 4 have more than 8 marbles.How many students have more than 5 marbles but less than 9 marbles?
A) 10 B. 11 C) 12 D) 13 E) None
Answer :
10 students have < 6 marbles
# 10 students have > 7 marbles
4 students have > 8 marbles
# 1 students have < 9 marbles
So 10+1 that is 11 (Ans.)
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A jogger running at 9 kmph alongside a railway track is 240 metres ahead of the engine of a 120 metres long train running at 45 kmph in the same direction.In how much time will the train pass the jogger ?
A) 3.6 sec B. 18 sec C) 36 sec D) 72 sec E) None
Answer :
MT=Initial separation/
Initial separation =240+120 that is 360 m
Relative speed =(45-9) kmph
=36*(5/18) that is 10 m/s
MT=360/10 that is 36 sec (Ans.)
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Arif sold 100 pens, of which 50 are red and 50 are black, at TK. 48 per pen.He made a profit of 20% on the black pens and made a loss of 20% on the red pens.what was the net gain on this sale ?
A) 0 B. -50 C) -100 D) -200 E) None
Answer :
Total SP=100*48 that is 4800
SP of red pen=50*48=2400
SP of black pen=50*48=2400
Total CP=2400*(5/
So Loss=200 (Ans.)
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7 years ago, Samir was 3 times as old as Saurov.In 4 years Samir will be twice as old as Saurov.What is Saurov’s present age?
A) 40 B. 18 C) 30 D) 20 E) None
Answer:
Approach-1:
Samir:Saurov =3:1 (7 yrs back)
Samir: Saurov =2:1 (After 4 yrs from present)
Age gap=7+4 that is 11
Samir age ratio gap=3-2 that is 1
ATQ 1==11
So 1 is also 11.
Saurov ‘s present age=11+7 that is 18 (Ans.)
Approach-2:
Saurov ‘s present age=S+7
Samir’s present age=3S+7
After 4 yrs:
3S+11=2(S+11)
=>S=11
So, Saurov ‘s age=S+7=11+7 that is 18 (Ans.)
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Box1 contains 500 marbles, 24% of which are black.Box2 contains some marbles of which 10% are black.You put the marbles together in another box and found that the percentage of black marbles is 20%.How many marbles were there in Box2?
A) 100 B. 150 C) 200 D) 250 E) None
Answer:
Approach-1:
Applying RoA :
24•••••••••••••
••••••••••••••2
=>10:4
=>5:2
ATQ 5==500
2==500*2/5 that is 200 (Ans.)
Approach-2:
24% of 500=120 are black
500-120 =380 are white
120+10% of x =20% of (500+x)
On solving, x=200 (Ans.)
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If -8<=x<=2 and -4<=y<=10 which of the following represents the range of all possible values of XY ?
Answer:
Possible values of XY are
1. (-8)*(-4)=32
2. 2*10=20
3. (-8)*10=-80
4. (-4)*2=-8
So, range is -80<=XY<=32 (Ans.)
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Raju has x number of books, which is 3 times as many as Siam and 1/2 As many as Payel.How many books do the three of them have altogether, in terms of x ?
A) 5x/6 B. 7x/3 C) 10x/3 D) 7x/2 E) None
Answer :
Raju has=x books
ATQ x=3*Siam
So Siam=(x/3) books
x==(1/2) of Piyal
So, Piyal =2x books
Cumulatively x+2x+(x/3) that is 10x/3 (Ans.)
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If y is an integer and 15<y<25, which of the following could be the average of 12,14,17,23 and y ?
A) 13.2 B. 15.6 C) 16.8 D) 18.2 E) 19.5
Answer :
Average value always lies in the middle.So, middle value is 17 which is near to 16.8 (Ans.)
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When a positive integer x is divided by 5 the remainder is 1. When x is divided by 8, the remainder is 4.What is the smallest positive integer y , such that (x+y) is divisible by 40?
A) 3 B.4 C) 9 D) 13 E) None
Answer :
If x=36 is taken thn all the conditions are satisfied.So, if x=36 then y must be 4 in order to divisible 36+4=40 by 40. So, y=4 (Ans.)
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At a certain bookstore,the regular price of each book is 20% less than it’s listed price.If during a sale, the price of each book at the store was 15% less than its regular price.The price of a book during the sale was what percent less than its listed price ?
A) 30% B) 32% C) 35% D) 38% E) None
Answer:
Approach-1:
LP:RP=5:4
RP:SP=20:17
LP:RP:SP=(5*20)
So 100-68 that is 32% less (Ans.)
Approach-2:
RP:LP=4:5
=80:100
During sale,
RP =80*(17/20) that is 68
So, LP=100
RP=68
So RP=32% less (Ans.)
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Silver is 26 times as heavy as Gold and Iron is 17 times as heavy as Gold.You have to prepare a mixture which is 23 times as heavy as Gold.what will be the ratio of Iron to silver in the mixture ?
A) 2:1 B. 2:3 C) 3:5 D) 1:2 E) None
Answer :
Applying RoA :
26•••••••••••••
••••••••••••23•
=>6:3
=>2:1 (Ans.)
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One year ago, the ratio of salary of Nasir and Gaurav was 5:8.Ratio between this year’s and last year’s salary of Nasir is 28:25 and the same for Gaurav’s is 23:20.If the sum of their present salary is TK. 1184, the difference between their present salary is :
A) TK. 448 B. TK. 340 C) TK. 288 D) TK.240 E) None
Answer :
Approach-1:
1 year Ago :
Ratio of N:G=5:8
=50:80
ATQ 25==50
28==50*28/25 that is 56
20==80
23==80*23/20 that is 92
Ratio of present salary:
N:G=56:92 or 14:23
ATQ 37==1184
9==1184*9/37 that is 288 (Ans.)
Approach-2:
25==5
28==5*28/25 that is 28/5 means 560%
Again 20==8
23==8*23/20 that is 46/5 means 920%
ATQ 1480%==1184
360%==1184*360/
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If x is an integer such that 5<x<11, 7<x<13 and x+2<12 then how many integers will satisfy x ?
A) 1 B. 2 C) 3 D) 4 E) None
Answer:
5<x<11
Here, 6,7,8,9,10 can be the value of x.
Again, 7<x<13
Here, 8,9,10,11,12 can be the value of x
Now, 8,9,10 are matched with both the conditions.
So, 8+2<12 ; 10<12 true
9+2<12 ; 11<12 true
10+2<12 ; 12<12 false
So there are two possible values of x (Ans.)
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John appointed 25 persons to complete a small bridge in 40 days. After 20 days, he appointed 15 more workers and the bridge was completed 5 days earlier.If he had not appointed additional workers by how many days he would have been behind the scheduled time ?
A) 2 B. 3 C) 4 D) 5 E) 7
Answer:
Applying MDH method :
25*40=25*20+40*
=>D=-4 days means 4 days behind the schedule (Ans.)
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At a certain club, the number of male members is twice that if female members.If 1/4 of male members are engineers and 1/5 of the female members are engineers, what fraction of the members are non-engineers ?
A) 13/25 B. 23/30 C) 2/5 D) 8/19 E) None
Answer: is attached in the comment box.
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Arif starts from A at 10 am towards B at 100 kmph.Babu starts from A at 10:10 am towards B at 120 kmph.Babu reached B 10 minutes before Arif.Calculate the distance between A and B
A) 100 B. 200 C) 240 D) 300 E) None
Answer:
Approach-1:
A:B=100:120 (Speed)
A:B=120:100 (Time)
ATQ 20==20
100==20*100/20 that is 100 minutes or 100/60 hr.
So D=120*(100/60) that is 200 km (Ans.)
Approach-2:
100*t=120(t-(1/
=>100t=120t-40
=>t=2 hr
So D=100*2 that is 200 km (Ans.)
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If ab<0 then all the following must be true EXCEPT
A) a/b<0 B. a^2+b^2>0 C) a^3+b^3<0 D) b/a<0 E) None
Answer :
We know that square always gives a positive value and cube always gives negative signs for the negative value.
So C is wrong due to its cube (Ans.)
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The cost of 12 pencils and 10 pens is 320.the cost of 20 pencils and 15 pens is 500.what is the difference between the cost of a pen and a pencil ?
A) 5 B. 10 C) 15 D) 20 E) None
Answer :
10 pen+12 pencil=320
=>2(5 pen+6 pencil)=320
=>5 pen+6 pencil=160•••(1
15 pen+20 pencil=500
=>5(3 pen+4 pencil)=500
=>3 pen+4 pencil=100•••(2
(1)*3-(2)*5 =>
15 pen+18 pencil=480
15 pen+20 pencil=500
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2 pencil=20
So, pencil =10
Pen=20
So, difference =20-10 that is 10 (Ans.)
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If x is an integer and y=-4x+17 what is the least value of x for which y is less than 1 ?
A) 2 B. 3 C) 4 D) 5 E) None
Answer:
If x=5 then y is less than 1
Ans. D
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Arif bought a pen at a 30% discount on listed price.Few months later , he found that the price for the same pen has increased by 50% and the discount he got in taka remained the same .How much discount did Arif get in terms of the new listed price ??
A) 10% B. 15% C) 20% D) 22.5% E) None
Answer :
LP=100
CP=70
Again LP=150
CP=150-30 that is 120
So, discount =(30/150)*100 that is 20% (Ans.)
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