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30 Jul 2024, 01:30
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
59% (02:36) correct
41%
(02:41)
wrong
based on 120
sessions
History
Date
Time
Result
Not Attempted Yet
Two players Lampard and Essien had a certain number of chocolates with them.If Lampard had 10 more than half the number of chocolates than Essien had,was the number of chocolates with Essien more than 20?
(1) The difference between the number of chocolates than Lampard and Essien had was less than 30.
(2) The total number of chocolates than Lampard and Essien had was greater than 5/2 of the number of the chocolates with Essien.
(1) The difference between the number of chocolates than Lampard and Essien had was less than 30.
(2) The total number of chocolates than Lampard and Essien had was greater than 5/2 of the number of the chocolates with Essien.
30 Jul 2024, 13:27
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IMO Answer B
L = 10 + 0.5E (given)
to find: E>20 or not
1) The difference between the number of chocolates than Lampard and Essien had was less than 30.
E=2; L=11.... diff less than 30
E=4; L=12.........."..............
.
.
E=20; L=20.......diff=0
E=40; L=30...... diff=10
INSUFFICIENT
2) The total number of chocolates than Lampard and Essien had was greater than 5/2 of the number of the chocolates with Essien.
L+E > 2.5E
L> 1.5E
10 + 0.5E >1.5E
10> E
SUFFICIENT
L = 10 + 0.5E (given)
to find: E>20 or not
1) The difference between the number of chocolates than Lampard and Essien had was less than 30.
E=2; L=11.... diff less than 30
E=4; L=12.........."..............
.
.
E=20; L=20.......diff=0
E=40; L=30...... diff=10
INSUFFICIENT
2) The total number of chocolates than Lampard and Essien had was greater than 5/2 of the number of the chocolates with Essien.
L+E > 2.5E
L> 1.5E
10 + 0.5E >1.5E
10> E
SUFFICIENT
31 Jul 2024, 01:37
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From the question stem one gets: \(l = 0.5e + 10\). From this, one can see that firstly, Essien must have an equal number of chocolates and secondly, if he has more than 20 chocolates it will have to be an even number greater than 21.
If Essien has over 20 chocolates, the minimum he will have is 22 chocolates. If he does, then Lampard will have 21.
(1) The difference between the number of chocolates than Lampard and Essien had was less than 30.
From the above, if Essien has 22 chocolates and Lampard has 21, then the difference will be 1 which holds with the above statement.
If Essien has 10 chocolates, then Lampard has 15. Here the difference is 5 which holds with the statement above.
Without further information it is impossible to solve for the question.
INSUFFICIENT
(2) The total number of chocolates than Lampard and Essien had was greater than 5/2 of the number of the chocolates with Essien.
Translating this into an equation: \(l + e > \frac{5}{2}e\)
PLUGGING IN \(l = 0.5e + 10\) INTO THE ABOVE:
\(0.5e + 10 + e > \frac{5}{2}e\)
\(10 > e\)
SUFFICIENT
ANSWER B
If Essien has over 20 chocolates, the minimum he will have is 22 chocolates. If he does, then Lampard will have 21.
(1) The difference between the number of chocolates than Lampard and Essien had was less than 30.
From the above, if Essien has 22 chocolates and Lampard has 21, then the difference will be 1 which holds with the above statement.
If Essien has 10 chocolates, then Lampard has 15. Here the difference is 5 which holds with the statement above.
Without further information it is impossible to solve for the question.
INSUFFICIENT
(2) The total number of chocolates than Lampard and Essien had was greater than 5/2 of the number of the chocolates with Essien.
Translating this into an equation: \(l + e > \frac{5}{2}e\)
PLUGGING IN \(l = 0.5e + 10\) INTO THE ABOVE:
\(0.5e + 10 + e > \frac{5}{2}e\)
\(10 > e\)
SUFFICIENT
ANSWER B
