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101 - 152 Inequalities

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101 - 152 Inequalities

by phoenix9801 » Tue Jul 13, 2010 3:32 pm
101- Material A costs $3 per kilogram, and Material B costs $5 per kilogram. If 10 Kilograms of Material K consists of x kilograms of Material A and y kilograms of Materials B, is x > y?


(1) y > 4

(2) the cost of the 10 kilograms of Material K is less than $40


Note: Can someone explain what is the question is really asking it so confusing. Is it asking x+y = 10????? Is there to use picking Numbers and please explain in details and simplest way...

I am unable to solve both statements.




152 - If Carmen had 12 more tapes, she would have twice as many tapes as Rafael. Does Carmen have fewer tapes than Rafael?

(1) Rafael has more than 5 tapes.

(2) Carmen has fewer than 12 Tapes.


Note: once I know that the questions is asking for C + 12 = 2R? So My question is how would you solve the (1) and (2) by using piking number or other alternative way to solve this prob,em. Please be simple when you explaining.
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by amising6 » Tue Jul 13, 2010 4:35 pm
phoenix9801 wrote:101- Material A costs $3 per kilogram, and Material B costs $5 per kilogram. If 10 Kilograms of Material K consists of x kilograms of Material A and y kilograms of Materials B, is x > y?


(1) y > 4

(2) the cost of the 10 kilograms of Material K is less than $40


Note: Can someone explain what is the question is really asking it so confusing. Is it asking x+y = 10????? Is there to use picking Numbers and please explain in details and simplest way...

I am unable to solve both statements.
this is yes or no type of question
question says 10 kg of material k=x kg of A+y kg of B i.e 10=x+y ...eq 1
cost of K=3*x+5*y .... eq 2
we know cost of A=3 and cost of B=5
we need to know quantity of A and B


statement 1)y>4
tis doesnt help much because y can be 5 in that case x will be 5 and thus x is not > then y
y can be 4.5 in that case x will be 5.5 so in this x>y so we have yes and no both
so staement 1 is insufficient on its own
statement 2)
the cost of the 10 kilograms of Material K is less than $40
so using eq 2 we will have 3x+5y<40 .....eq3
x+y=10 multiplying both side by 3 we have 3x+3y=30 replacing this value in eq3
3x+5y<40
3x+3y+2y<40
30+2y<40
so 2y<10
y<5
and we know x+y=10 so X will always be greater than 5 and thus x>y
so statement 2 is sufficient
in this case if you choose A to be
.
c d bold part
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by amising6 » Tue Jul 13, 2010 4:45 pm
152 - If Carmen had 12 more tapes, she would have twice as many tapes as Rafael. Does Carmen have fewer tapes than Rafael?

(1) Rafael has more than 5 tapes.

(2) Carmen has fewer than 12 Tapes.


Note: once I know that the questions is asking for C + 12 = 2R? yes this is right So My question is how would you solve the (1) and (2) by using piking number or other alternative way to solve this prob,em. Please be simple when you explaining

now let us assume carmen had C tapes if she had 12 more tapes i.e C+12=2R .... eq 1(twice as many tapes as Rafael)we need to find C<R
staement 1)Rafael has more than 5 tapes.if Rafael had 6 tapes then from equation 1 Carmen will have 0 tapes(w can assume positive integer as this is tapes)
at the same time if Rafael had 15 tapes carmen will have 30 -12-18 tapes
so we have situtaion were w have yes answer as well as no answer so insufficient
statement 2) Carmen has fewer than 12 Tapes. i.e C>12
so again put value for C in eq 1 so lets assume C to be 11
in that case R will turn out to be 11.5
least value which R can have is 12
so R wille greate than C hence 2 is sufficient answer B
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