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19 Aug 2014, 20:34
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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:
95%
(hard)
Question Stats:
48% (02:53) correct
52%
(02:58)
wrong
based on 136
sessions
History
Date
Time
Result
Not Attempted Yet
A mobile phone is available for $39000 cash or $17000 as down payment followed by five equal monthly instalments of $4800 each. The simple rate of interest per annum under the instalment plan would be
A: 18%
B: 19%
C: 21.2%
D: 21.81%
E: 22.07%
Source: CMAT Preparation
A: 18%
B: 19%
C: 21.2%
D: 21.81%
E: 22.07%
Source: CMAT Preparation
21 Aug 2014, 13:59
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PareshGmat
Dear PareshGmat,
I'm happy to respond
but I have a few criticisms of this question. I am not familiar with this particular source. First of all, GMAT questions all are scrupulously realistic in terms of the numbers they use in a problem. Perhaps if the currency were something other than US dollars, these numbers would be plausible, but the idea of a mobile phone that costs $39,000 is not realistic in the least -- most automobiles cost less than that! That's one aspect that is not GMAT like. Also, NOBODY walks around with $39,000 in cash on them. That would be wads and wads of bills.
Second, the answers are very close together --- if the answers were spread out, we could use estimation, which the GMAT often would employ in a problem of this sort. See:
https://magoosh.com/gmat/2012/the-power- ... mat-quant/
In order to get the exact answer here, presumably one would need a calculator or have to do tedious long division --- this is another aspect that is quite unlike the GMAT.
Finally, in my calculation, I get an answer very different from the answers here.
Under the installment plan, we pay 5*(4800) = 24,000 plus $17,000 for a total of $41,000. That means, we pay $2000 more under the installment plan than we would have paid up front in cash. I understand the question to ask --- the extra $2000 would be what percent of interest on the original $39,000 cost? That would be
2000/39,000 *100% = 2/39 * 100%
Well, 2/40 = 1/20 = 0.05 = 5%. If we make the denominator smaller, the whole fraction gets bigger. Thus,
2/39 should be slightly larger than 5%
Indeed, a calculator gives
2/39 = 5.1282051282 ...%
None of the answer choices are in this range. Something is funny here.
Mike
22 Aug 2014, 02:13
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Hi
Simple interest SI = (P*R*T)/100
where P is the principal amount
R is the rate of interest
and T is time in years
the way I see it: on down payment of 17,000, customer is not paying any interest. it is the remaining sum which will be paid for 5 months that will bear an interest. Therefore, the principal amount for which interest is being charged is 39,000 - 17,000 = 22,000
For this 22,000 a total sum of 5*4800 = 24,000 was pain. (Time is five months, so T = 5/12, as T is in years.)
thus, SI = 2000 or
2000 = (P*R*T)/100
2000 = (22,000*R*5)/(100*12)
R = (2,000*12*100)/22,000*5
R = 21.81%
Therefore answer is D
Simple interest SI = (P*R*T)/100
where P is the principal amount
R is the rate of interest
and T is time in years
the way I see it: on down payment of 17,000, customer is not paying any interest. it is the remaining sum which will be paid for 5 months that will bear an interest. Therefore, the principal amount for which interest is being charged is 39,000 - 17,000 = 22,000
For this 22,000 a total sum of 5*4800 = 24,000 was pain. (Time is five months, so T = 5/12, as T is in years.)
thus, SI = 2000 or
2000 = (P*R*T)/100
2000 = (22,000*R*5)/(100*12)
R = (2,000*12*100)/22,000*5
R = 21.81%
Therefore answer is D
