How to ace Advanced Mathematics for IPM

In this article, we will discuss the trends, patterns, commonly asked questions and the strategy to ace the Quantitative Aptitude section of the IPM examination. In the IPM aptitude test, quantitative ability section has 60 questions. This section is generally a mix of all the topics of quant and a few topics of logical reasoning.
A majority of the questions, which appeared in this exam over the previous years, have been from the topics like Number system and Algebra.  In the last IPM exam there were around 25 – 28 questions from these two areas only.  The other important areas from where the questions appeared are Arithmetic, Permutation, Combination & Probability, Geometry and Mensuration, Trigonometry and Set Theory. There were a few questions from Miscellaneous Quant. There were 8 – 10 questions from logical reasoning as well. In the arithmetic area the questions were from ratio & proportion, percentage and time and work.  Last year there were 2- 3 questions without options wherein the students had to type the answer in the space provided.
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The level of difficulty of questions in this section is usually high. There are one or two logical reasoning blocks in this section, and they are of moderate difficulty level. Just to give you a fair idea, here are a few of the actual questions from the previous years’: 
Q1. Four women and one man plan a robbery and decide to share the spoils equally. However, on the night of the robbery, the man falls sick. While the robbery is successful, the man gets only half of the share he was entitled to. Then, the ratio of amount of money shared by the women to the original share they were entitled to is:
a. 7:6
b. 8:7
c. 9:8
d. 10:9
Solution: As there are five persons, they all have entitled to 1/5th share. This means the four women together are supposed to take a total of 4/5th share. Now, after the robbery the man was given half of the share, he was entitled to i.e. ½ of 1/5 = 1/10th of the total, that means the remaining 9/10th was shared by the women. Now, the question asked about the share taken by the women, to the original share women were entitled for. That can be found as 9/10 : 4/5 ⇒ 9/10 : 8/10 ⇒ 9 : 8.
Q2. The number of different six digit numbers, the sum of whose digits is odd is:
a. 106/2
b. 6!×106
c. 9×105
d. 45×104
Solution: The total numbers of six-digit numbers are 9 × 105. As all the numbers are consecutive, every odd number is followed by even number and vice versa. Now based on the same logic half of the numbers will have their sum as even and half of the numbers will have their sum as odd. Thus the required numbers will be half of 9 × 105, which is equal to 45 × 104. This same question if you try to solve mathematically you can spend 3 – 4 min. on this question.
Q3. “In an office, there are 15 males and 10 females. Three employees are selected at random. What is the probability that 1 female and 2 males are selected?”
This is a relatively simple question based on Probability and anyone who has basic knowledge of the topic can solve it comfortably.
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To conclude, as the difficulty level of this section is moderate to high, one should be selective in attempting the questions. You should revise the topics like Numbers and Algebra in detailed manner as 40 – 50% of the total questions appeared from this area. At the same time do not ignore the other quantitative areas as the examiner can ask questions from any area. Besides that, the revision of logical reasoning areas could also prove to be of great help. Do remember the following important points while attempting the quantitative ability section of the paper.
  • You may not be able to attempt all the questions from this section. Thus, be selective and attempt only questions related to the areas you are comfortable with.
  • Any competitive paper is not meant to be attempted in the order given in the test. You should always work as per your strengths in that paper.
  • It is better to scan the questions and then start solving it.
  • Attempting the same kind of questions first, which you have done/seen earlier in the mocks would be a better strategy.
  • Never spend more than 2 – 3 min on any question. This habit is to be developed while solving the mock papers. 
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The above mentioned tricks and strategy would definitely help you to perform better in the quantitative section of the IPM exam. Good luck!
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