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13 Feb 2024, 02:30
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
61% (03:12) correct
39%
(03:19)
wrong
based on 237
sessions
History
Date
Time
Result
Not Attempted Yet
At a certain store, all notebooks have the same price and all pencils have the same price. The price of four notebooks and three pencils is more than $12 and less than $13. The price of two notebooks and five pencils is more than $8 and less than $9. If a notebook costs x more than a pencil, which of the following could be the value of x ?
(A) $0.60
(B) $1.05
(C) $1.30
(D) $2.20
(E) $2.70
(A) $0.60
(B) $1.05
(C) $1.30
(D) $2.20
(E) $2.70
13 Feb 2024, 12:11
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Option D should be correct
Suppose, cost of a notebook = a; cost of a pencil = b
From the question we know 12 < 4a+3b < 13 ; 8 < 2a+5b < 9 ; a = b+x
So, 12 < 4(b+x)+3b < 13 => 12 < 7b+4x < 13 ....(1)
and 8 < 2(b+x)+5b < 9 => 8 < 7b+2x < 9 .....(2)
The way I do a substraction in inequalities is I swap the values, so after (1)-(2) it becomes :
(12 - 9) < (7b+4x)-(7b+2x) < (13 - 8)
=> 3 < 2x < 5 => 1.5 < x < 2.5
Only option D (2.20) satisfies
Suppose, cost of a notebook = a; cost of a pencil = b
From the question we know 12 < 4a+3b < 13 ; 8 < 2a+5b < 9 ; a = b+x
So, 12 < 4(b+x)+3b < 13 => 12 < 7b+4x < 13 ....(1)
and 8 < 2(b+x)+5b < 9 => 8 < 7b+2x < 9 .....(2)
The way I do a substraction in inequalities is I swap the values, so after (1)-(2) it becomes :
(12 - 9) < (7b+4x)-(7b+2x) < (13 - 8)
=> 3 < 2x < 5 => 1.5 < x < 2.5
Only option D (2.20) satisfies
General Discussion
13 Feb 2024, 04:32
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IMO answers is (D)
let price of pencil is p and price of notebook is n
we are given n= x+p
12<4n+3p<13
8<2n+5p<9
Put value of x
12<7p+4x<13 ....(1)
8<7p+2x<9 changes sign -9<-7p-2x<-8 ....(2)
add both equation (1) & (2)
3<2x<5 that means 1.5<x<2.5
let price of pencil is p and price of notebook is n
we are given n= x+p
12<4n+3p<13
8<2n+5p<9
Put value of x
12<7p+4x<13 ....(1)
8<7p+2x<9 changes sign -9<-7p-2x<-8 ....(2)
add both equation (1) & (2)
3<2x<5 that means 1.5<x<2.5
