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CAT 2019 Quant – Slot 2

Q.1) If 5^x-3^y=13438 and 5^(x-1)+3^(y+1)=9686 then find x+y.

a)13

b)14

[bg_collapse view=”button-blue” color=”#ffffff” expand_text=”Correct Answer” collapse_text=”Show Less” ]a)13[/bg_collapse] [bg_collapse view=”button-orange” color=”#4a4949″ expand_text=”View Solution” collapse_text=”Show Less” ]

Solution:

Here we can go by hit n trial

13438 is 5 digit number so 5^x must be a 5 digit number

5^6=15625

So putting x=6 in the first equation we get 3^y=2187

So y=7

Putting this in eq 2

5^5 +3^8=3125+6561=9686

So x+y=6+7=13

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Q.2) 

a)0

b)10

c)1

d)-1

[bg_collapse view=”button-blue” color=”#ffffff” expand_text=”Correct Answer” collapse_text=”Show Less” ]c)1[/bg_collapse] [bg_collapse view=”button-orange” color=”#4a4949″ expand_text=”View Solution” collapse_text=”Show Less” ]

Solution:

a1=1

a1-a2=2

a2=-1

a1-a2+a3=3

a3=1

a1-a2+a3-a4=4

a4=-1

1,-1,1,-1….so on

so sum of every two consecutive terms will be 0

so only a1023 will remain which is odd numbered term  having value 1

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Q.3) Amal invests Rs 12000 at 8% interest, compounded annually, and Rs 10000 at 6% interest, compounded semi-annually, both investments being for one year. Bimal invests his money at 7.5% simple interest for one year. If Amal and Bimal get the same amount of interest, then the amount, in Rupees, invested by Bimal is

a)20920

b)10920

[bg_collapse view=”button-blue” color=”#ffffff” expand_text=”Correct Answer” collapse_text=”Show Less” ]a)20920[/bg_collapse] [bg_collapse view=”button-orange” color=”#4a4949″ expand_text=”View Solution” collapse_text=”Show Less” ]

Solution:

Interests for both are same so equate their interests

Semi-annually for Amal so rate becomes half  (i.e.3% )and time will become double i.e. 2 years

Interest for Amal= (12000*8*1)/100 +10000[1.03]^2 -10000

Interest for Bimal= (P*7.5*1)/100

960+609=(7.5P)/100

156900=7.5P

P=20920

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Q.4) Anil alone can do a job in 20 days while Sunil alone can do it in 40 days. Anil starts the job, and after 3 days, Sunil joins him. Again, after a few more days, Bimal joins them and they together finish the job. If Bimal has done 10% of the job, then in how many days was the job done?

a)14

b)15

c)13

d)12

[bg_collapse view=”button-blue” color=”#ffffff” expand_text=”Correct Answer” collapse_text=”Show Less” ]c)13[/bg_collapse] [bg_collapse view=”button-orange” color=”#4a4949″ expand_text=”View Solution” collapse_text=”Show Less” ]

Solution:

Work=lcm(20,40,3)=120

A=6 units per day

S=3 units per day

Anil does =6*3=18 units in 3 days

Bimal does 10% of the job=12 units 

So anil and sunil will do 90% of the job=108 units

Anil  has already done 18 units 

So anil and sunil will do 90 units in, Say X days

So

X(A+S)=90

Putting values of A and S

X=10 days

So B will also work for 10 days

So total=3+10=13 days were required to complete the work

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Q.5)