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10 Feb 2021, 05:25
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Difficulty:
85%
(hard)
Question Stats:
57% (03:19) correct
43%
(03:03)
wrong
based on 84
sessions
History
Date
Time
Result
Not Attempted Yet
Iqbal dealt some cards to Mushtaq and himself from a full pack of playing cards and laid the rest aside. Iqbal then said to Mushtaq "If you give me a certain number of your cards, I will have four times as many cards as you will have. If I give you the same number of cards, I will have thrice as many cards as you will have." Of the given choices, which could represent the number of cards with Iqbal?
A. 9
B. 31
C. 12
D. 35
E. 39
A. 9
B. 31
C. 12
D. 35
E. 39
12 Feb 2021, 03:18
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Let the number of cards that Mushtaq has = M and the Number that Iqbal has = I
Let the number of cards given either ways be = n
If Mushtaq gives Iqbal n cards, then Iqbal has I + n cards and Mushtaq has M - n cards
Given that I + n = 4 * (M - n) ... (1)
If Iqbal gives Mushtaq n cards, then Iqbal has I - n cards and Mushtaq has M + n cards
Given that I - n = 3 * (M + n) ... (2)
Adding (1) and (2), we get 2I = 4M - 4n + 3M + 3n
2I = M - n ... (3)
Subr=traction (2) from (1), we get 2n = 4M - 4n - 3M - 3n
2n = M - 7n
M = 9n
Substituting in (3), we get 2I = (7 * 9n) - n = 62n
Therefore I = 31n
The number of cards Iqbal has will be a multiple of 31 and only option B satisfies the same.
Option B
Arun Kumar
Let the number of cards given either ways be = n
If Mushtaq gives Iqbal n cards, then Iqbal has I + n cards and Mushtaq has M - n cards
Given that I + n = 4 * (M - n) ... (1)
If Iqbal gives Mushtaq n cards, then Iqbal has I - n cards and Mushtaq has M + n cards
Given that I - n = 3 * (M + n) ... (2)
Adding (1) and (2), we get 2I = 4M - 4n + 3M + 3n
2I = M - n ... (3)
Subr=traction (2) from (1), we get 2n = 4M - 4n - 3M - 3n
2n = M - 7n
M = 9n
Substituting in (3), we get 2I = (7 * 9n) - n = 62n
Therefore I = 31n
The number of cards Iqbal has will be a multiple of 31 and only option B satisfies the same.
Option B
Arun Kumar
25 Apr 2024, 23:36
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Hi CrackverbalGMAT - not understanding your explanation here. How do you move from M=9n to substituting that in equation (3), which is 2I=M-n, and re-writing that as 2I=(7*9n)-n? Where does the 7 come from? Wouldn't it now be 2I=9n-n=8n, so I=4n, in which case the answer would be 12, as that's the only multiple of 4 in the answer choices? I'm confused how you made this leap to multiply 9n by 7 when plugging into equation (3). Please clarify.
