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Bunuel
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Mary bought a number of pencils. If each pencil was either a 24-cent 15 Jan 2025, 01:30
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35% (medium)

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65% (01:17) correct 35% (01:14) wrong based on 86 sessions

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Mary bought a number of pencils. If each pencil was either a 24-cent pencil or a 30-cent pencil, how many 24-cent pencils did Mary buy?

(1) The total price of the pencils Mary bought was 102 cents
(2) Mary bought a total of 4 pencils

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Mary bought a number of pencils. If each pencil was either a 24-cent 15 Jan 2025, 04:31
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1. A alone as for only one combination 3*24+1*30 = 102 possible.
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Mary bought a number of pencils. If each pencil was either a 24-cent 15 Jan 2025, 08:07
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1. 24 x + 30 y = 102

Now only one pair of x and y satisfy this equation

X=3 y=1

Hence, sufficient

2. Total pencil were 4

Not sufficient since many combination would be there
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Mary bought a number of pencils. If each pencil was either a 24-cent 15 Jan 2025, 08:32
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IMO Ans is A
Each pencil was either a 24-cent pencil or a 30-cent pencil, how many 24-cent pencils did Mary buy?

Statement I: The total price of the pencils Mary bought was 102 cents

Let there be x 24 cent pencils, and y 30 cent pencils.
Now, the equation becomes:
24*x + 30*y = 102

Checking the units digit of the total, we require a 2. Irrespective of the value of y, 30*y shall yield a 0 in units place. Hence, we require a 3 from 24*x.
Our options can be:
4*3 = 12
4*13 = 52.....( However 24*13 exceeds 102, hence there can be no numbers higher than 3).

substituting in (i),
x= 3, y= 1

Statement II: Mary bought a total of 4 pencils
It tells us only that x+y =4.
Hence there can be several values of x and y:(1,3)(3,1)(2,2) etc.
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Bunuel
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